Molecular Ecology (2011) 20, 768–783
doi: 10.1111/j.1365-294X.2010.04979.x
Are low but statistically significant levels of genetic
differentiation in marine fishes ‘biologically
meaningful’? A case study of coastal Atlantic cod
H . K N U T S E N , * † E . M . O L S E N , * † P . E . J O R D E , † S . H . E S P E L A N D , * C . A N D R É ‡
and N . C . S T E N S E T H * †
*Institute of Marine Research, Flødevigen, N-4817 His, Norway, †Centre for Ecological and Evolutionary Synthesis (CEES),
Department of Biology, University of Oslo, P.O. Box 1066 Blindern, N-0316 Oslo, Norway, ‡Department of Marine EcologyTjärnö, University of Gothenburg, S-45296 Strömstad, Sweden
Abstract
A key question in many genetic studies on marine organisms is how to interpret a low
but statistically significant level of genetic differentiation. Do such observations reflect a
real phenomenon, or are they caused by confounding factors such as unrepresentative
sampling or selective forces acting on the marker loci? Further, are low levels of
differentiation biologically trivial, or can they represent a meaningful and perhaps
important finding? We explored these issues in an empirical study on coastal Atlantic
cod, combining temporally replicated genetic samples over a 10-year period with an
extensive capture–mark–recapture study of individual mobility and population size. The
genetic analyses revealed a pattern of differentiation between the inner part of the fjord
and the open skerries area at the fjord entrance. Overall, genetic differentiation was weak
(average FST = 0.0037), but nevertheless highly statistical significant and did not depend
on particular loci that could be subject to selection. This spatial component dominated
over temporal change, and temporal replicates clustered together throughout the 10-year
period. Consistent with genetic results, the majority of the recaptured fish were found
close to the point of release, with <1% of recaptured individuals dispersing between the
inner fjord and outer skerries. We conclude that low levels of genetic differentiation in
this marine fish can indeed be biologically meaningful, corresponding to separate,
temporally persistent, local populations. We estimated the genetically effective sizes (Ne)
of the two coastal cod populations to 198 and 542 and found a Ne ⁄ N (spawner) ratio of
0.14.
Keywords: Atlantic cod, dispersal, effective population size, tagging, temporal genetic stability
Received 23 September 2010; revision received 18 November 2010; accepted 25 November 2010
Introduction
In the early years of fishery research, the discovery of a
pelagic larval phase for most fish species of economic
concern led to the widespread belief that the ocean is
demographically open and that species are typically
panmictic over their range (reviewed in Jennings et al.,
2001). This view was only mildly challenged by the first
population genetic analyses of marine fishes, which typCorrespondence: H. Knutsen, Fax: +47 370 59001;
E-mail: halvor.knutsen@imr.no
ically found low levels of genetic divergence. Statistically significant differences were only detected over
considerable geographical distances (e.g. Grant & Utter
1984; Ryman et al. 1984; Mork et al. 1985) or for polymorphisms that are probably under natural selection
(Sick 1965; Fevolden & Pogson 1995). With the advent
of more highly polymorphic molecular markers (particularly microsatellites), improved statistical techniques,
and in some cases improved sampling design, a growing literature (e.g. Jones et al. 1999; Ruzzante et al.
1999; Nesbø et al. 2000; Knutsen et al. 2003; Mathews
2007; McCairns & Bernatchez 2008) has challenged the
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B I O L O G I C A L L Y R E L E V A N T G E N E T I C S I G N A L S 769
generality of panmixia in marine species. Instead, these
studies coincide in finding that marine fishes are subdivided into genetically separated units at various geographical scales, leading towards a paradigm shift in
the view of population structuring in marine fishes
(Hauser & Carvalho 2008).
A common denominator of most genetic studies of
marine organisms is the low levels of genetic differentiation, FST, among putative populations (Ward et al. 1994;
Waples 1998; Waples & Gaggiotti 2006). A number of
explanations for this observation have been put forward.
The most common one by far is that gene flow is higher
in marine than in terrestrial and freshwater organisms
(Ward et al. 1994). Other suggestions for a low FST are
recent origin of populations (see postglacial expansion
Pogson et al. 1995; Pampoulie et al. 2008), large effective
population sizes (Ward et al. 1994) and selective sweeps
(Árnason 2004). In addition, the generally higher level of
genetic variation (gene diversity, H) in marine organisms may also limit the absolute level of FST (Hedrick
1999). However, studies have shown that although the
level of H varies among loci, FST estimates may frequently still not be very high (Gregorius et al. 2007).
Restricted genetic differentiation introduces a challenge when interpreting positive findings, i.e. statistically
significant differentiation, in terms of population substructure. When true differentiation is low or absent, various sources of errors may assume a relatively greater
importance, possible leading to false conclusions (Waples
1998). These potential sources of errors include nonrandom sampling of individuals (e.g. sampling family or kin
aggregations, see Allendorf & Phelps 1981; Hansen et al.
1997), temporal fluctuations in allele frequencies (random
genetic drift, see Turner et al. 2002; Selkoe et al. 2006),
natural selection (Nielsen et al. 2006; Nilesen et al. 2009a)
and genotype scoring errors (Bonin et al. 2004). Such
potential errors have led some authors to question the
emerging paradigm of an abundant population substructuring in marine fishes (e.g. Nilesen et al. 2009a).
Atlantic cod has been given much attention in genetic
studies over nearly five decades, and substructuring of
the species has been revealed at increasingly finer geographical scales. After early works found significant
genetic differentiation at the trans-Atlantic scale (Mork
et al. 1985; Árnason 2004), Bentzen et al. (1996) detected
genetic differentiation at a scale of 200 km, and Hutchinson et al. (2001) found structure in the southern part
of the North Sea at a comparable scale. Ruzzante et al.
(1999) found structure among large spawning aggregations off Canada, and O’Leary et al. (2007) made similar
observations among spawning areas in the central and
eastern part of the North Atlantic. Genetic differentiation were later detected at even finer geographical
scales in coastal cod, first at a few dozen kilometres
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(Knutsen et al. 2003) and then later narrowed down to
the level of individual fjords (Jorde et al. 2007). Ecological studies on egg distribution (Knutsen et al. 2007) and
egg density in relation to fjord circulation patterns
(Ciannelli et al. 2010; Cnickle & Rose 2010) have provided a possible explanation for population structure
by documenting the retention of pelagic cod eggs
within fjords. Behavioural studies have further demonstrated that coastal cod tend to have a high degree of
site fidelity and restricted home ranges (Dannevig 1954;
Espeland et al. 2008). A life history study using the
method of probabilistic maturation reaction norms to
disentangle phenotypic plasticity from evolution suggests that life history traits of coastal cod have evolved
at a spatial scale comparable to the substructure
revealed by microsatellites (Olsen et al. 2008).
Nevertheless, the biological relevance of small genetic
differences in cod and other marine species is still largely unknown and under debate. The potential for
selective forces acting on molecular allele frequency
patterns should not be dismissed out of hand, even for
presumed selective neutral markers. Convincing arguments have been raised for selection operating on the
polymorphisms in cod at loci Hb1 (Andersen et al.
2009) and PanI (Karlsson & Mork 2003; Pogson & Fevolden 2003). Evidence has also been presented for selective effects on microsatellites (e.g. the Gmo132 locus),
most likely through hitchhiking with linked genomic
regions (Karlsson & Mork 2005; Nielsen et al. 2006).
Recent scans of large panels of SNP markers indicate
that up to 10% of cod genes could be under selective
pressures in at least some part of the species’ range
(Moen et al. 2008; Nielsen et al. 2009b; Bradbury et al.
2010). Nonrandom sampling and temporal genetic
change are also potential confounding factors in genetic
studies of cod, as reported levels of genetic divergence
are on the order of the inverse of sample sizes. Systematic temporal sampling using several year-classes, in
combination with ancillary ecological information, is
recommended to ensure the correct biological interpretation of genetic differentiation patterns (Hedgecock
et al. 2007).
Here, we apply a decade of temporal genetic data,
together with several years of tagging data on Atlantic
cod, both within and outside a fjord along the Norwegian Skagerrak coast to explore the biological meaning
of genetic substructuring on a fine geographical scale.
Materials and methods
Study species
The Atlantic cod (Gadus morhua) is one of the most commercially important marine fishes in the world (FAO
770 H . K N U T S E N E T A L .
2000). It is distributed along vast coastlines from the
waters of the continental shelf in the North Atlantic,
extending northwards to Disco Bay and Spitsbergen
and southwards to Cape Hatteras and the Bay of Biscay. In the eastern Atlantic, the species also enters the
Baltic Sea.
Atlantic cod have several strategies with regard to
spawning. Typically, coastal cod are stationary and
complete their entire life cycle within a restricted geographical area. In contrast, cod belonging to oceanic
populations may perform long-distance spawning
migrations and release eggs and larvae that are carried
with ocean currents back to the nursery grounds. Cod
is a broadcast spawning species, with females producing and releasing more than one million eggs per kilogram of somatic body weight under good nutritional
conditions (Wroblewski et al. 1999). Eggs are pelagic
and hatch within 3 weeks depending on temperature.
Larvae are still pelagic after hatching and stay in the
water column and feed on zooplankton until they metamorphose into bottom-settled small fish (juveniles),
when they are approximately 3–5 cm long.
Sampling
Sampling of young-of-year (referred to as age 0+ or age
class 1 cod for genetic analysis) was carried out by
means of a beach seine between June and September on
a semi-annual basis from 1996 to 2005 (Table 1) from
inside the Søndeled Fjord and among the skerries at the
entrance to the fjord, at the Risør archipelago (Fig. 1).
Approximately 100 fish were collected from each area
and year and stored frozen ()20C) until genetic analyses. The sampling sites within the fjord represent a sheltered area where cod eggs seem to be retained by ocean
currents (Espeland et al. 2007; Knutsen et al. 2007; Ciannelli et al. 2010). On the other hand, sampling localities
in the skerries represent an area that is largely exposed
to the open ocean of the Skagerrak and the North Sea.
Previous genetic studies have included a sample of
adult cod from this locality that displayed no statistical
difference from North Sea cod (based on eight loci,
Knutsen et al. 2004, p. 1340). We included these adult
samples from the skerries and the North Sea (collected
in 2000, 2001, 2002) in the present study as references
for possible origins of juveniles. In addition, a sample
of adult cod from within the Søndeled Fjord was collected by nets and is also included in the present study.
Genetic analysis
Microsatellite DNA polymorphisms were screened in
all samples as follows. We applied a Viogene Inc. miniprep system for DNA extraction from muscle tissue cut
from whole frozen specimens. PCR conditions for the
detection of 13 microsatellites largely followed the procedure described in the original papers: Gmo2 and
Gmo132 (Brooker et al. 1994); Gmo3, Gmo8, Gmo19,
Gmo34, Gmo35, Gmo36 and Gmo37 (Miller et al. 2000);
Tch5, Tch12, Tch13 and Tch22 (O’Reilly et al. 2000),
applying Qiagen Taq polymerase in the reactions. PCR
fragments were separated and scored on a Beckman
Table 1 The sampled localities and summary statistics for genetic variability within sites. HS is the estimate of gene diversity; FIS
measures deviation from Hardy–Weinberg genotype proportions (P-values for two-sided tests). Also indicated are the number of loci
that appear to have excesses and deficiencies of heterozygotes
Sample
Juvenile samples
Fjord 1996j
Fjord 1997j
Fjord 1998j
Fjord 2004j
Fjord 2005j
Skerries 1998j
Skerries 2001j
Skerries 2004j
Skerries 2005j
Adult samples
Skerries 2000ad
Fjord 2005ad
North Sea 2002ad
North Sea 2000 ⁄ 01ad
N loci
excess
N loci
deficit
Stage
Sample
size
HS
Juv.
Juv.
Juv.
Juv.
Juv.
Juv.
Juv.
Juv.
Juv.
100
100
100
99
100
100
100
98
100
0.674
0.697
0.707
0.692
0.691
0.709
0.692
0.701
0.719
0.057*
)0.007
0.012
0.031
0.023
0.020
)0.001
0.019
0.006
4
7
7
6
5
5
5
6
7
9
6
6
7
8
8
5
7
6
Adult
Adult
Adult
Adult
101
88
100
101
0.710
0.717
0.719
0.711
0.014
)0.013
0.018
0.018
8
8
3
6
5
5
10
7
FIS
*P < 0.05. Note that this sample is significant owing to one locus only, Gmo 35.
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58°46'30"N
58°43'30"N
58°40'30"N
9°3'0"E
9°9'0"E
9°15'0"E
9°21'0"E
9°27'0"E
Fig. 1 Map identifying sample locations both inside and outside a Norwegian fjord on the Skagerrak coast. Red circles identify sheltered locations inside the fjord, whereas black circles give exposed localities in the outer skerries. The fjord sill is given as a small
solid black line crossing the fjord. The bathymetry is coarsely given with light blue colours for shallow water and dark blue colours
for deeper waters.
SEQ 8000 automatic DNA analyser. Two trained persons independently scored all genotypes, and disagreements on genotype scorings were resolved following a
rescreening of the sample. The majority of the 13 loci
were routinely scored with minor disagreements,
although Gmo132 and Tch13 were highly polymorphic,
displayed a moderate amount of PCR stuttering and
required several PCR reruns before consistent genotype
scorings were obtained. Genotypes were analysed with
the Microchecker software (Van Oosterhout et al. 2004)
to check for null alleles or potential technical artefacts,
and none were found.
The amount of genetic variability was characterized
by gene diversity (HS within samples, HT in the total:
Nei & Chesser 1983) and the observed number of alleles
at each locus. Deviations from Hardy–Weinberg genotype proportions within loci were estimated by FIS (estimator f of Weir & Cockerham 1984) and tested for
using the exact probability test in the GENEPOP software
(ver. 4.0: Rousset 2008).
Spatial patterns in the genetic structure among juvenile cod were characterized using several approaches.
First, the magnitude of spatial genetic difference among
the main areas within the fjord and the skerries was
compared with temporal fluctuations among sample
years with AMOVA, using the Arlequin software (Excoffier
et al. 2005). Second, pairwise genetic differences (FST,
estimated and averaged over loci as described by Rousset 2008) were calculated for all sample pairs and tested
2010 Blackwell Publishing Ltd
for significance using exact tests of allele frequency differences with GENEPOP (using 10 000 dememorizations
and batches, and 10 000 iterations per batch). FST values
were also bootstrapped over loci to provide the 95% CI
using the software GDA (Lewis & Zaykin 2001). Each
locus was tested separately, and a joint P-value over loci
was calculated by summarizing twice the negative logarithms of the single-locus P-values, evaluated against the
critical chi-square value with 2 · 13 degrees of freedom
(i.e. Fisher’s summation procedure). Finally, we calculated genetic distances among samples (DA: Nei et al.
1983) and visualized the results by applying multidimensional scaling (MDS) in XL-STAT (Addinsoft).
The potential effects of particular loci were investigated by estimating FST and HT for each locus between
the fjord and skerries areas, lumping temporal samples.
The evidence for natural selection, identified as outlier
loci, was tested for by a simulation-based approach
(Beaumont & Nichols 1996) implemented in the LOSITAN
selection detection workbench (Antao et al. 2008). The
test aims at identifying loci that have been subject to
selective forces. It does this by comparing each locus’
FST value with those expected under selective neutrality
under two alternative mutation models (stepwise mutation and the infinite allele models), given its observed
HT value. The expectations are derived by computer
simulations, and we performed 10 000 replicates. No
qualitative differences were observed between the two
mutation models.
772 H . K N U T S E N E T A L .
Temporal changes in allele frequencies among juvenile cohorts were characterized with Jorde & Ryman’s
(2007) estimator Fs’ and used to estimate the genetically
effective sizes of putative populations. We adopted and
extended the method of Jorde & Ryman (1995) to estimate Ne from diverse cohort data (see Appendix).
Sample pairs of the same temporal duration (i.e.
cohorts born with the same number, j, of years apart)
were combined in mean Fj’s (i.e. average Fs’ over loci
and pairs of temporal samples) and corrected for the
effects of overlapping generations and number of years
apart as:
Fcorr ¼
Fj G
Cj
Here, and in the following, the F’s are corrected for
sampling by assuming sample plan II (Jorde & Ryman
2007, Eq. 13), and we omit apostrophes on estimates for
simplicity. G is the generation length (in years) and the
Cj’s are correction factors for overlapping generations,
specific to each temporal interval j. G and Cj were calculated from demographic data (age-specific survival
and birth rates) as outlined in the Appendix, and we
assume that the demographic characteristics are similar
for the two populations and use the same set of correction factors for both. Finally, mean Fcorr values were calculated by averaging over all sampling intervals to
estimate the (variance) effective population size:
Ne ¼
1
:
2Fcorr
Standard errors (SE) for Fcorr and Ne were calculated by
jackknifing over loci, leaving out one locus at a time.
From the r = 13 replicate jackknife estimates, Fjack, we
calculated the mean Fjack (which is nearly identical to
Fcorr ) and its standard error (Efron & Tibshirani 1993,
Eq. 11.3–11.4). Finally, 95% confidence intervals for the
estimated Ne were calculated from SE for Fjack by
assuming that Fjack is normally distributed:
95% CI Ne ¼
1
2Fjack 1:96SE
.
Capture–mark–recapture analysis
In addition to the genetic sampling programme outlined previously, an independent capture–mark–recapture study was conducted in the Søndeled fjord and
the skerries outside the fjord (Espeland et al. 2008).
Here, we used these data to estimate census population
size within the fjord (not including age 0 fish) and also
to detect movement of fish between the fjord and the
skerries. For this purpose, the fjord sill (a natural shallow section across the fjord, 19–30 m, separating deeper
basins inside and outside) was defined as the border
between the two areas. Cod were captured in traps in
shallow water (at a depth of 1–5 m) in collaboration
with a local fisher during late spring (May and June) in
2005–2007. Individual cod were measured to the nearest cm, and each fish was individually tagged with an
external T-bar anchor tag (Hallprint, Australia) positioned parallel to the anterior dorsal fin. To facilitate
the return of tags from cod harvested by fishers, each
tag had a printed return address and reward. All fish
were released alive at the point of capture immediately
after being tagged and measured for length, with each
trap usually containing 1–3 cod. As a result, our
approach ensured that a small number of tagged cod
were released throughout the study area, which
allowed us to draw an inference on the total population. Each year, we tagged cod throughout the environmental gradient stretching from the innermost
sheltered areas of the Søndeled Fjord system to the
outer skerries and most exposed parts of the Risør
Archipelago. We received tags partly from dead recoveries (harvested fish) and partly from live recaptures
made by local eel fishers (as bycatch). The eel fishers
were paid to measure and release any tagged cod,
thereby providing us with additional data on individual cod dispersal. Using data from all three sampling
years, out-fjord dispersal was defined as fish that were
tagged while inside the sill and later recaptured outside the sill. Similarly, in-fjord dispersal was defined as
fish that were tagged outside the sill and recaptured
inside. Census population size (NC) was estimated
based on information from multiple sampling occasions
within the 2007 season, using the Lincoln–Petersen
approach and adjusting for the small sample size
(McCallum 2000):
Nc ¼
ðn1 þ 1Þðn2 þ 1Þ
1
ðr þ 1Þ
where n1 is the number of cod captured and tagged on
the first sampling occasion, n2 is the number of cod captured and examined for marks during the second occasion and r is the number of cod tagged on the first
occasion and then recaptured during the second occasion. We focused on the 2007 sampling season because
we consistently sampled the inner Søndeled Fjord in
this year on four occasions during a relatively short
time period (May). The spatial extent of this sampling
conformed to the spatial extent of the inner fjord
genetic sampling programme (c.f. Figs 1 and 2). In 2005
and 2006, sampling was less consistent in the inner part
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B I O L O G I C A L L Y R E L E V A N T G E N E T I C S I G N A L S 773
of the fjord, and the number of within-season recaptures was sparse. Consequently, we did not estimate
the census population size for these years.
The capture–mark–recapture data were also used to
estimate the total number of mature fish (spawners)
within the inner fjord. The proportion of mature fish in
the samples could not be directly determined because
all fish were released alive after tagging and their maturity state was unknown. However, we were able to estimate the proportion of spawners in our samples from a
length-based maturity ogive that was developed from a
recent study on cod in this inner fjord system. In this
previous study (Bråthen Lund 2008), both the length
and the maturity state (juvenile or spawner) were determined for each fish. A length-based maturity ogive was
then developed using logistic regression. We used the
parameter estimates from this model to estimate the
probability for being mature (based on individual’s
measured length) and assigned a maturity state to each
fish. For example, the maturity ogive had an L50 (the
length where the fish reached a 50% probability of
being mature) of 35 cm, so a fish of this size would fall
into the mature category with a 50% probability. A
smaller fish of 30 cm would only have a 20% probability of being classified as mature, while a larger fish of
40 cm would have an 80% probability of being classified as mature. From these assigned maturity states, we
estimated the total number of spawners (NS) in the
inner fjord as:
NS ¼ NC p;
where NC is the estimated census population size and p
is the fraction of the fish in our samples that were
assigned a mature state.
(a)
Results
Genetic variability patterns
Altogether, 1,287 individual cod, including 897 juveniles
(age 0+) and 390 adults (age >1+), were genotyped at
the 13 microsatellite loci (Table 1). Genetic variability
varied among loci, with observed heterozygosity (HO,
averaged over samples) ranging from 0.228 (at locus
Gmo3) to 0.930 (Tch 5), and number of alleles ranging
from 7 (Gmo36) to 56 (Gmo8) (data not shown).
With the exception of the 1996 fjord sample of juveniles, none of the samples showed any significant deviations from the Hardy–Weinberg genotype expectations
(Table 1). In the deviating 1996 fjord sample, the deviation arose from a single locus (Gmo35), which displayed
a highly significant deficiency (uncorrected for multiple
tests) of heterozygotes. Overall, nine loci of 117 comparisons (juvenile samples) were significant. None of the
significances did remain, however, after applying tablewide Bonferroni corrections for multiple tests. No null
alleles or evidence for technical artefacts was detected
by Microchecker at any locus.
The outlier (Beaumont) test did not reveal any evidence for the selection operating on any of the 13
microsatellite loci (Fig. 3). Instead, P-values were not
significant for any locus and ranged between 0.48
(Gmo19) and 0.85 (Gmo 132).
The AMOVA analysis revealed a significant variance
between juvenile samples from inside the Søndeled
Fjord and those from the skerries, with no significant
proportion of the total variance attributed among years
within groups (Table 2). With reference to pairwise FST
estimates (Table 3), the highest level of divergence
(about 0.01) was consequently observed between a sam-
(b)
Fig. 2 Movement of tagged cod between the Søndeled Fjord and the surrounding Risør archipelago, showing the (a) out-fjord dispersal of cod tagged inside the main sill in the Søndeled Fjord, and the (b) in-fjord dispersal of cod tagged outside the sill. Black circles = tagging locations and green circles = recapture locations of fish tagged inside the fjord. Red circles = recapture locations of fish
tagged outside the fjord. The shaded polygons highlight fish dispersing across the fjord sill. One individual (not shown) moved outfjord and was recaptured near the town of Kragerø, 20 km to the northeast of the Søndeled Fjord.
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774 H . K N U T S E N E T A L .
difference is highly significant (P << 0.0001) and is also
significant at eight of 13 loci considered separately
(Table 4). In contrast, FST among temporal replicates
within groups, and between juvenile and adults within
groups, were generally lower, and many or most
of them were not statistically significant (c.f. Table 3).
The MDS plot (Fig. 4) visualizes these findings and
ple from within the fjord and samples from the skerries
or the North Sea. Of 42 such pairwise sample comparisons, all but four were statistically significant or highly
so (c.f. Table 3). On average, the FST estimate between
the fjord and skerries locations, lumping temporal samples, was 0.0037 with a 95% bootstrap confidence interval from 0.0017 to 0.0060 (Table 4). This average
0.60
FST
0.40
0.20
GMO3
TCH12
0
0
0.20
0.40
He
GMO35
GMO34
GMO36
TCH22
0.80
0.60
GMO8
GMO37
GMO132
GMO19
GMO2 TCH13
TCH5
0.95
Fig. 3 Plot of FST versus heterozygosity (He) to identify potential loci subject to hitchhiking selection. Light grey area: 95% CI for
neutrality. The analysis is based on juvenile cod inside the Søndeled Fjord and at exposed skerries, c.f. Fig. 1.
Table 2 Results of AMOVA analysis partitioning genetic variability among juvenile samples into among localities (inner fjord and
outer skerries) and within localities (temporal replicates) components
Source of variation
df
Sum of
squares
Variance
components
Fixation
index
Between localities (outside vs. inside)
Among year-classes within localities
Within samples
1
7
1783
2.883
)52.359
4660.037
0.012
)0.051
2.614
0.005
)0.020
)0.015
P-value
0.009 (±0.0009)
1
Table 3 Genetic differentiation (FST) between pairs of samples (below diagonal) and exact tests for differentiation (above diagonal,
not corrected for multiple tests)
Fjord samples
Fjord1996j
Fjord1997j
Fjord1998j
Fjord2004j
Fjord2005j
Fjord2005ad
Skerries1998j
Skerries2001j
Skerries2004j
Skerries 2005j
Skerries2000ad
North Sea 2002ad
North Sea 2000 ⁄ 01ad
Skerries samples
1996j
1997j
1998j
2004j
2005j
2005ad
–
0.0010
0.0010
0.0027
0.0028
0.0016
0.0034
0.0061
0.0051
0.0043
0.0033
0.0054
0.0055
0.2748
–
0.0019
0.0064
0.0039
0.0037
0.0048
0.0107
0.0080
0.0100
0.0051
0.0115
0.0077
0.3147
0.0628
–
0.0039
0.0032
0.0005
0.0045
0.0082
0.0085
0.0087
0.0045
0.0068
0.0064
0.0070
0.0000
0.0142
–
0.0037
0.0044
0.0027
0.0049
0.0040
0.0033
0.0027
0.0049
0.0035
0.1028
0.0007
0.0261
0.0003
–
0.0012
0.0030
0.0017
0.0017
0.0026
0.0018
0.0030
0.0023
0.0398
0.0010
0.1614
0.0000
0.0664
–
0.0028
0.0041
0.0060
0.0071
0.0014
0.0051
0.0039
1998j
2001j
North Sea samples
2004j
0.0363 0.0005 0.0008
0.0205 0.0000 0.0000
0.0028 0.0000 0.0000
0.0387 0.0000 0.0000
0.0100 0.1661 0.0159
0.0128 0.0020 0.0000
–
0.0009 0.2435
0.0014 –
0.1190
0.0002 0.0001 –
0.0033 0.0001 0.0009
)0.0001 0.0021 0.0015
0.0012 )0.0012 0.0001
)0.0006 0.0000 0.0001
2005j
2000ad
0.0004
0.0000
0.0000
0.0001
0.1275
0.0000
0.0003
0.4434
0.0441
–
0.0021
0.0006
0.0024
0.0025
0.0000
0.0003
0.0000
0.0177
0.0751
0.3610
0.0169
0.0005
0.0001
–
0.0001
0.0003
2002ad 2000 ⁄ 2001 ad
0.0008
0.0000
0.0000
0.0000
0.0226
0.0001
0.0318
0.8656
0.1506
0.0158
0.7022
–
)0.0009
0.0005
0.0000
0.0000
0.0001
0.0910
0.0013
0.2123
0.0680
0.2016
0.0002
0.3414
0.8592
–
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B I O L O G I C A L L Y R E L E V A N T G E N E T I C S I G N A L S 775
From the inner part of Søndeled Fjord, the five semiannual juvenile samples yielded a total of 10 pairs of
cohorts for estimating genetic drift. Corrected for overlapping generations and years between samples (see
Appendix), the average estimate over all cohort pairs in
the inner fjord was 0.00253 (Table 5). The corresponding point estimate of the genetically effective size of this
fjord population is Ne = 1 ⁄ (2 · 0.00253) = 198. A jackknife estimate of standard error (SE) for this point estimate was 0.00111, yielding lower (2.5%) and upper
(97.5%) confidence limits for Ne of 106 and 1423,
respectively (Table 5). The finite upper limit is consistent with the finding of significant allele frequency differences between at least some cohort pairs (c.f.
Table 3). From the sampled area in the skerries, six
pairs of cohorts were available and gave a mean estimate, corrected for overlapping generations and years
between samples, of 0.00092 (SE = 0.00048). This corresponds to an estimate of Ne = 542 (with a 95% CI from
269 to infinity) for the skerries population.
separates samples from within the fjord on one side
from those in the skerries and the North Sea on the
other. Both the MDS plot and the table of pairwise FST
values fail to distinguish between samples of coastal
cod in the skerries from adult samples in the North Sea
(including samples taken off Hirtshals and from the
North Sea proper, c.f. Fig. 4, Table 3).
Table 4 Spatial genetic differentiation (FST) between the inner
fjord and the skerries, and exact test for significance (c.f. Fig.
1.)
Locus
Spatial differentiation
inside vs. outside
Gmo2
Gmo3
Gmo8
Gmo19
Gmo34
Gmo35
Gmo36
Gmo37
Gmo132
Tch5
Tch12
Tch13
Tch22
All loci
95% CI (0.0017–0.0060)
FST
P-value
0.0028
0.0183
0.0080
0.0080
0.0050
0.0039
0.0017
0.0043
0.0088
)0.0004
0.0039
0.0003
)0.0007
0.0037
0.040
<<0.0001
<<0.0001
0.009
0.007
<0.0001
0.428
0.005
<0.0001
0.640
0.180
0.944
0.295
<<0.0001
Capture–mark–recapture estimates of dispersal and
population size
A total of 2427 cod were tagged and released during
the 2005–2007 study period (N2005 = 739, N2006 = 823,
N2007 = 865). The mean length of all released fish was
40 cm (range: 16–86 cm). A total of 1055 of these fish
were tagged and released in the inner part of the Søndeled Fjord (inside the sill, Fig. 1), while the remaining
1372 fish were tagged and released in the outer part of
0.04
Kruskal’s stress = 0.278
Fjord 2004J
Skerries 2005J
0.02
Skerries 2004J
Skerries 1998J
Dim2
Fjord 1997J
0
North Sea 2000/01ad
–0.04
–0.02
0
Fjord 2005J
0.02
0.04
Fjord 1998J
North Sea 2002ad
Skerries 2001J
–0.02
Skerries 2000ad
Fjord 1996J
Fjord 2005ad
–0.04
Dim1
Fig. 4 Patterns of geographical structure in coastal Atlantic cod revealed by multidimensional scaling (MDS) of the matrix of genetic
distances (DA; Nei et al. 1983; Kruskal’s stress = 0.278). Note that the first axis clearly separates exposed and sheltered locations for
all temporal samples (explaining 31% of the variation), (explaining 29% of the variation).
2010 Blackwell Publishing Ltd
776 H . K N U T S E N E T A L .
Table 5 Observed temporal allele frequency shifts (Fj) among juvenile cod cohorts and estimates of effective size (Ne) of the cod
populations in the Søndeled fjord and the skerries. Fj are averaged over 13 microsatellite loci and over cohort pairs born the same
number (j) of years apart, calculated according to Jorde & Ryman 2007 (equation 13; corrected for sampling according to sample plan
II). Fcorr,j are Fj’s adjusted for overlapping generations and number of years apart by multiplying each Fj with the factor G ⁄ Cj, where
G = 4.28 and Cj = 6.77, 8.56, 8.54, 9.01, 10.23, 11.57, 12.35, 13.12 and 14.60, for j = 1–9 years apart, respectively (Appendix). SE are
standard errors for Fcorr, calculated by jackknifing over loci. Ne is the per-generation effective population size, estimated as the
inverse of 2Fcorr. 95% confidence intervals (CI) for Ne were calculated from SE for Fcorr (¥ = infinity, representing a negative estimate
of genetic drift)
Years apart (j)
Søndeled fjord*
1
2
6
7
8
9
All
95% CI
Skerries†
1
3
4
6
7
All
95% CI
Number of pairs
Fj
Fcorr,
3
1
1
2
2
1
10
0.00447
0.00221
0.00798
0.00958
0.00683
0.00567
0.00282
0.00110
0.00295
0.00332
0.00223
0.00166
0.00253
(0.00190)
(0.00170)
(0.00153)
(0.00157)
(0.00077)
(0.00098)
(0.00111)
1
2
1
1
1
6
0.00193
0.00165
0.00033
0.00057
0.00667
0.00122
0.00082
0.00015
0.00021
0.00231
0.00092
(0.00083)
(0.00114)
(0.00066)
(0.00076)
(0.00067)
(0.00048)
j
(SE)
Ne
177
453
169
151
224
301
198
106–1423
409
606
3235
2362
216
542
269–¥
*Søndeled fjord juvenile samples include cohorts 1996 (sample size, n = 100), 1997 (n = 100), 1998 (n = 100), 2004 (n = 99) and 2005
(n = 100) (representing 5 · (5)1) ⁄ 2 = 10 cohort pairs).
†Skerries juvenile cohorts 1998 (n = 100), 2001 (n = 100), 2004 (n = 98) and 2005 (n = 100) (6 cohort pairs).
the Søndeled Fjord and the Risør Archipelago (Fig. 2).
A total of 784 (32.3%) tagged fish were seen again at
least once, either as a live recapture or as a dead recovery, and for which precise information about the tag
and the point of recapture ⁄ recovery was provided. An
additional 73 tags were reported without sufficient
information as to the point of recapture ⁄ recovery, and
these additional observations are not included in the
results presented here. A total of 13 (i.e. 13 ⁄ 1055 = 1.2%
over the 3-year period) fish tagged in the inner Søndeled Fjord were later caught in the outer areas (i.e.
representing fish moving out of the fjord). All but one
of these potentially dispersing individuals were found
in the outer part of the Søndeled fjord or in the Risør
archipelago (Fig. 2). A total of nine (i.e. 9 ⁄ 1372 = 0.7%
per 3 years) fish tagged in the outer areas were later
caught in the inner Søndeled fjord (i.e. fish moving into
the fjord). Assuming that these movements represent a
permanent dispersal, and not just temporary excursions,
the average exchange between putative inside and outside fjord populations can be taken as the proportions
of recaptured fish that moved between the two locations, or 1.7% and 1.0% per generation, for outward
and inward dispersal, respectively. Most likely, we
present a minimum estimate of dispersal because the
tag reporting rate is likely to be less than one, and
because fish could also have dispersed without being
detected. On the other hand, many dispersal events are
likely to be only temporarily. For instance, our data
show that most dispersed fish were recaptured fairly
close to the border between the inner fjord and the
skerries, indicating that this dispersal only represent
small-scale movement around the mouth of the fjord.
The total population size of cod in the inner Søndeled
Fjord in 2007 was estimated to 1847 individuals
(SE = 533, 95% CI = 800–2893), not including juveniles
(age 0+). Owing to the low sample size, this estimate
was based on pooling two release occasions (May 14
and 21, pooled n1 = 149) as well as two recapture occasions (May 25 and 31, pooled n2 = 123). During the last
two occasions, we recaptured a total of nine cod that
had been tagged and released during the first two occasions (r = 9). Based on the probability of being mature
at length, we estimated that 75% of the fish caught in
the inner Søndeled fjord during 2007 (N = 316, mean
size = 43 cm, range: 27–66 cm) were mature fish (spawners). From this, the total number of potential spawners
in the inner fjord was estimated at 1391. The observed
2010 Blackwell Publishing Ltd
B I O L O G I C A L L Y R E L E V A N T G E N E T I C S I G N A L S 777
ratio of effective size to number of spawners in this
population is thus Ne ⁄ N = 198 ⁄ 1391 = 0.14.
Discussion
By combining extensive sampling and genetic screenings with capture–mark–recapture data on coastal cod,
we were able to identify a temporally persistent substructuring of the species over a range of only a few
dozen kilometres. The identified structure had a rather
low level of genetic differentiation (average FST =
0.0037; 95% CI: 0.0017–0.0060), which was nevertheless
highly statistically significant, occurred over multiple
temporal samples and apparently did not depend on
loci subject to selection.
The finding of statistically significant allele frequency
differences among samples is in itself not sufficient for
safe conclusions regarding population substructuring.
Because the statistical power is high when using multiple, highly polymorphic markers and reasonably large
sample sizes (Ryman et al. 2006), minor allele frequency
differences that are unrelated to population structure –
and thus not ‘biologically meaningful’ in this context –
can achieve statistical significance (Waples 1998). What
is of particular concern is that effects of nonrandom
sampling or natural selection could be generating the
weak differentiation observed among samples. In this
study, we have dealt with these concerns by repeated
temporal sampling and statistical analyses of divergence patterns among loci, coupled with independent
estimates of fish dispersal.
Among the most problematic sources of error is nonrandom sampling, especially when dealing with juveniles. Juvenile fishes of many species appear in family
clusters, and if the sampling covers a restricted area,
the sample may contain a large proportion of one or a
few families only (Hansen et al. 1997; Buston et al.
2009). With different samples containing different families, a spatial pattern of genetic differentiation may
appear, even if all families belong to the same biological
population. While cod have pelagic eggs and larvae,
and family clustering in this species seems less likely
than in, e.g. reed-building species, it is conceivable that
some form of nonrandom family distribution could be
maintained in the pelagic phase by ocean current
advection. Poor family mixing in the plankton has been
suggested as being responsible for the observed ‘chaotic
genetic patchiness’ in other marine fishes (Selkoe et al.
2006). In the present study, we minimized such risks by
sampling more than one site from each of the two areas
(c.f. Fig. 1) and by sampling each area over several
years. The genetic pattern that emerges from our data,
as depicted in the MDS plot (Fig. 4), is that juvenile
samples tend to cluster according to geographical loca 2010 Blackwell Publishing Ltd
tion and together with adult samples from the same
area. Such a pattern is unlikely to arise by chance and
strongly implies segregation into genetically differentiated units or populations.
Natural selection is a potentially powerful agent in
modifying the spatial distribution of allelic variants
(Conover et al. 2006). Atlantic cod has an extensive distribution throughout the North Atlantic, where it
encounters widely different environmental conditions,
e.g. in terms of temperature and salinity. It is therefore
not surprising that strong evidence for the operation of
natural selection has accumulated at some loci for this
well-studied species. The present study deals with cod
within a restricted geographical range, and environmental differences are likely to be small in comparison with
those encountered by conspecifics inhabiting different
parts of the distribution range. Nonetheless, some environmental differences do occur between the inner fjord
and that of the outer skerries: the inner Søndeled Fjord
being characterized by a relatively low water visibility
(Secci depth) and low oxygen concentration compared
to the outer coast (Johannessen & Dahl 1996). We
searched for evidence for natural selection operating on
the 13 microsatellite loci, either directly or through
hitchhiking, by statistically comparing the magnitudes
of differentiation among loci (Fig. 3). No such evidence
was found, and the differentiation between the fjord
and skerry areas was reasonably similar among loci (c.f.
Table 4). In total, eight of the 13 loci were statistically
significant at the 5% level or better. Gmo8, Gmo34 and
Gmo132 have been suggested in other studies (Nielsen
et al. 2006; Nilesen et al. 2009a) of not being selectively
neutral, e.g. in comparisons among the Barents Sea and
Newfoundland or against the North Sea. Although
these loci do not stand out as prone to selection in the
present study, leaving them out still leaves five significant loci. Hence, we find no evidence for the observed
structure being caused by selected loci. An absence of a
selective pattern in Gmo132 was also noted by Nielsen
et al. (2006) for the North Sea, geographically close to
this study area. This absence could indicate that the
alleged selective forces are weak in this geographical
area or that the genomic background is different. This
of course does not exclude the possibility that selection
are operating in other, unlinked, parts of the genome
and that the populations are adapted to their respective
local environment.
A major strength of the present study is the independent assessment of fish movement between the
inner fjord and the outer coast by capture–mark–recapture methods. We acknowledge that this method will
rely on a number of assumptions, including spatial
homogeneity in fishing pressure and tag reporting
rates. Still, the estimated proportions of fish dispersing
778 H . K N U T S E N E T A L .
(1.7% outward and 1% inward per generation) demonstrates that adult dispersal in this population system
is restricted enough to explain the lack of genetic
homogeneity among populations. Indeed, this low dispersal is predicted to eventually (over a few hundred
generations) lead to a level of genetic differentiation
between the two populations of FST = 0.04 (based on
computer simulations), which is several times the
observed level of 0.0037. Additional dispersal can,
however, also occur at the earlier life stages (i.e. pelagic eggs and larvae), as revealed by a recent study of
cod egg-transport in a neighbouring fjord. Measuring
egg density and water transport in and out the fjord
in all depth layers, Ciannelli et al. (2010) found evidence for temporarily short pulses of water (and eggs)
transport out the fjord, while the general pattern was
an inward transport, thus maintaining partial isolation.
A strong tendency for egg retention within fjords has
also been reported by other studies on coastal cod
(Bradbury et al. 2000, 2003; Espeland et al. 2007; Knutsen et al. 2007). Such retention may be a prerequisite
for maintaining genetically distinct inner fjord populations in this species.
The local cod population inhabiting the inner fjord
apparently has a limited number of spawners
(Ns = 1391) and a limited genetically effective population size (Ne = 198). Such estimates are quite uncertain,
as judged by their wide confidence intervals, and are
further subject to a number of assumptions that are not
all fully met. In particular, gene flow among populations could bias estimates of Ne, either up or down,
depending on whether gene flow is continuous or irregular (Wang & Whitlock 2003). In the present case, the
proportions of migrants were low (1.0 to 1.7%), and
genetic difference between residents and immigrants
was small (FST = 0.0037), indicating that any effect (i.e.
bias) of gene flow on the estimated Ne should be minor
(c.f. Wang & Whitlock 2003; Palstra & Ruzzante 2008).
We infer a ratio of effective size (per generation) to
number of spawners (per season), Ne ⁄ Ns = 0.14, for the
fjord population. This estimate is nearly identical to the
median ratio reported for a wide range of organisms
(Palstra & Ruzzante 2008). On the other hand, our estimate is considerably higher than the exceedingly low
values, of orders 10)5 to 10)3, reported for some marine
fishes (e.g. Turner et al. 2002; Hutchinson et al. 2003).
Possibly, our higher value indicates a less pronounced
effect of ‘sweepstakes’ chances (c.f. Selkoe et al. 2006) in
reproduction in more sheltered coastal and fjord habitats when compared to the open sea. Nevertheless, it
seems clear that coastal cod populations could be relatively small, both numerically and effectively, and are
nearly isolated and may thus be vulnerable to local
overexploitation.
The cod population inhabiting the outer skerries was
less well characterized in this study. This population is
probably larger numerically than the fjord population,
but an estimate is not possible from available data. The
point estimate of Ne is also much larger (545, as compared with 198) but, as expected for the temporal
method, this larger point estimate is associated with a
greater uncertainty (the confidence interval includes
infinity as an upper limit). A second problem relates to
delimiting the geographical extent of this population as
it is not physically restrained to the same extent as the
fjord population. Indeed, as judged by our genetic findings (large Ne estimate and apparently no differentiation
with adult North Sea cod), it is possible that this skerries population is simply a fragment of the North Sea
stock. However, ripe fish are observed in this locality,
and it seems clear that local spawning is taking place
among skerries. The most likely explanation at the
moment therefore is that this represents a local population that receives substantial gene flow from the North
Sea by passive drift of eggs and larvae with ocean currents (Knutsen et al. 2004; Stenseth et al. 2006).
In conclusion, we have shown that a weak level of
differentiation in coastal cod most likely represents two
separate biological populations. One population of limited, actual and effective size inhabits the inner, sheltered part of the fjord, where it apparently completes
its life cycle, while a larger population that genetically
resembles and may possibly represent a segment of the
North Sea cod stock inhabits the skerries outside the
fjord. As an indicator for demographically largely independent biological populations, the weak differentiation
observed herein (average FST = 0.0037) is therefore seen
as being highly biologically relevant. Attempts at generalizing ‘biologically meaningful’ levels of genetic divergence (Waples 1998) should proceed with caution, and
‘meaningful’ needs to be evaluated with respect to the
biological question at hand.
Acknowledgements
This work was funded by the Research Council of Norway
through the projects ‘Dynamics and genetics of oceanic—coastal
cod population complexes’ and ‘Linking physics and biology—Structuring of cod populations in the North Sea ⁄ Skagerrak
water-system.’ Further funding was provided by The Norwegian Ministry of Fishery and Coastal Affairs and the University
of Oslo (through the Centre for Ecological and Evolutionary
Synthesis, CEES) and FORMAS. We are grateful to colleagues
for the provision of tissues samples (Tore Johannessen, Svein E.
Enersen, Øystein Paulsen, Petter Baardse and Jan Atle Knutsen).
Further, we thank Kate Enersen, Hanne Sannæs and Anna-Karin
Ring for their technical assistance in the laboratory. We also
thank Helge Larsen, Hanne Sannæs, Lena Omli and Even Moland for assisting with the capture and recapture of tagged cod.
2010 Blackwell Publishing Ltd
B I O L O G I C A L L Y R E L E V A N T G E N E T I C S I G N A L S 779
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All co-authors share an interest in understanding the mechanisms that drive population structure in marine organisms. This
paper resulted from interactions among all co-authors, with
the primary aim of examining focal mechanisms that promote
and maintain the genetic population structure in coastal Atlantic cod. Such information will provide management with useful
information in the context of sustainable use of marine
resources.
Appendix
Estimating effective size from cohort genetic data
The relationship between genetic drift and effective population
size (Ne) is complicated for species with overlapping genera 2010 Blackwell Publishing Ltd
tions such as Atlantic cod. Previously, Jorde & Ryman (1995)
devised a set of expressions that allow us to compute a ‘correction factor’ from demographic data that can be applied for estimating Ne from observed temporal allele frequency shifts
among consecutive cohorts. No such expressions are available,
however, for the situation when samples are drawn from
cohorts born more than 1 year apart, as is the case for most of
those screened herein. This Appendix describes the estimation
of demographic parameters used in Jorde & Ryman’s (1995)
procedure and an extension of that procedure to cohorts born
more than 1 year apart, using computer simulations.
Demographic parameters
The elements of a standard Leslie population matrix were estimated from available catch data from coastal cod from several
locations along the Norwegian Skagerrak coast. Annual surveys of cod have been carried out in this area during the
autumn (November) for a number of years (2001–2005). Altogether, eight localities were annually surveyed (from east to
west: Hvasser, Hvaler, Jomfruland, Flødevigen, Høvåg, Mandal, Korshamn and Farsund) with trammel nets (Olsen et al.
2008). These locations bracket, but do not include, the Søndeled
Fjord. Other surveys have been conducted over the years for
various purposes in the Søndeled fjord as well (c.f. Gjøsæter &
Danielsen 2010 and references therein), but these surveys have
typically covered different times of the year (when assessment
of maturity is difficult) and ⁄ or have applied different sampling
gears. There does not seem to be large differences in demography among Skagerrak coastal cod populations, and we elected
to use the most reliable data set for our purposes, which is the
collated set for eight localities.
Surveyed fish were killed, measured, weighted, aged (from
otolith growth zones), sexed and classified according to maturity. Prior to estimating demographic parameters, we lumped
fish of both sexes from all eight localities for a total of n = 3066
individuals with complete records. The annual survival rate (S,
assuming survival to be constant for all age classes, i) was estimated from the lumped numbers of individual’s catch data
(ni,, Fig. A1a) by linear regression of log(ni) on age class i,
ignoring the youngest (clearly underrepresented in the sample)
and oldest age classes (very low counts, c.f. Fig. A1a). The estimated regression slope of the log number of fish in each age
class was b = )0.8346 (Fig. A1b), corresponding to an annual
survival rate of S = eb = 0.434. From the estimated S, agespecific survival rates were calculated as li = Si)1 (Table A1).
Age-specific birth rates, bi, were estimated in a two-step
approach. First, we estimated the probability of being mature
from the observed proportions of mature fish in each age class,
using logistic regression (glm function in the R statistical package). The logistic regression of maturity (binary response) on
age class (Fig. A1c) indicated that most fish matured when
aged 1+ to 3+, thus making them 2 years or older when their
first offspring were born. Second, we used average body size
(body weight) as a proxy for reproductive success and predicted average body weight for each age class from the linear
regression of individual body weights on age class. There was
an apparent linear gain in body weight, and presumably reproductive output, per year (Fig 4d), with a slope of 550.8 gram ⁄ year (Fig. A1d). The bi was calculated by multiplying the
782 H . K N U T S E N E T A L .
6
5
4
3
0
1
2
log (number of fish)
7
1500
(b)
Number of fish
500
1000
(a)
8
9 10
(d)
Body weight (g)
0.2
4
6
Age class
8
10
2
4
6
Age class
8
10
0
0.0
2
5000
5 6 7
Age class
3000
4
1000
3
prob (mature)
0.4 0.6 0.8
(c)
2
1.0
1
2
4
6
Age class
8
Fig. A1 Demographic data and parameter estimates for Norwegian Skagerrak coastal cod. (a) Number of cod collected in late
autumn (November) from 2001 to 2005 from six localities. Black = immature; grey = mature (i.e. cod presumed to spawn in the following spawning season, early spring). (b) Estimation of annual survival, S, by means of regressing log(N) on age class. Here, we
omit early, clearly under-recruited, age classes (i = 1) and older classes (i > 9) with few observations (open symbols). Slope = )0.8346.
(c) Estimation of probability of maturing at age, by means of logistic regression of proportion of mature individuals in each age class.
(d) Average body weight for each age class, used to estimate relative number of offspring per parent and age class. See text for
details.
Table A1 Estimated demographic parameters (life table) for
coastal cod populations, based on conjugated data from eight
sample localities along the Norwegian Skagerrak coast. li and
bi are the age-specific survival and birth rates, respectively,
and were estimated from catch data as described in the text
i
li
bi
pi = li*bi
1
2
3
4
5
6
7
8
9
10
1
0.43403
0.18838
0.08177
0.03549
0.01540
0.00669
0.00290
0.00126
0.00055
0.005
0.217
1.316
3.333
5.096
6.525
7.842
9.131
10.414
11.695
0.005
0.094
0.248
0.273
0.181
0.101
0.052
0.026
0.013
0.006
estimated probability of being mature at age i with the average
body weight for that age class and adjusted so as to result in a
P
population of constant size, i.e.
li*bi = 1. The estimated
parameters (li and bi) are presented in Table A1. During all
calculations, we progressed age to the upcoming breeding
season (in the spring) so that age 0+ (zero) fish captured during the autumn surveys were treated as age class 1 and so on
for older fish. The product pi = li*bi can then be interpreted at
the probability of an individual (e.g. daughter) having a parent
(mother) that was i years old when the individual was born.
P
As a result, the generation length is G =
pi*i = 4.28 years for
these coastal cod populations.
Computer simulations
The estimated age-specific demographic parameters, li and bi
(Table A1), were assumed to be representative for both focal
populations and used to infer two important genetic characteristics of the populations, viz. average generation length, G and
a vector with elements, ‘correction factors’ Cj, which are
needed to relate observed temporal differences among cohorts
born various numbers of years apart (j) to the per-generation
effective population size, Ne. The generation length is calculated as described earlier, although no analytic expressions are
available for Cj, except for j = 1 (Jorde & Ryman 1995; Eq.
10–13 and 23). We therefore resorted to computer simulations
to derive numerical values for Cj for all j = 1–9. The simulations were carried out as follows. The simulated population
consisted of a series of 10 discrete age classes (i), each containing a number of 2*Ni = 2*N1*li genes. We arbitrarily chose
2010 Blackwell Publishing Ltd
B I O L O G I C A L L Y R E L E V A N T G E N E T I C S I G N A L S 783
P
N1 = 1000, for a total population size of N =
Ni = 1765 individuals (or 3530 genes). Survival from age class i to i+1 was
simulated by randomly drawing 2*Ni+1 surviving genes without replacement from the 2*Ni genes present in age class i.
Reproduction was simulated by random drawing of 2*Ni*bi
P
from age class i, for a total of
Ni*bi = N1 = 1000 newborns
entering the population each year. After an initial period of
t = 50 years, a sampling of genes for genetic analyses was simulated with a random drawing of 100 genes with replacement
(sample plan II, Nei & Tajima 1981; Waples 1989) from age
class 1 for each of 10 consecutive years, t = 51–60. This simulation procedure was replicated 100 000 times, representing
100 000 independently inherited loci, and used to calculate
average temporal allele frequency shifts, Fj (Jorde & Ryman
2007; Eq. 13), over pairs of cohorts born j = 1–9 years apart
(the estimator is called Fs’, but we use j as a subscript here to
2010 Blackwell Publishing Ltd
indicate that the estimates refer to cohorts born j years apart,
and we drop the apostrophe for simplicity). These simulated
frequency shifts were used to calculate the vector of correction
factors, Cj = Ne*G*2*Fj (c.f. Jorde & Ryman 1995; Eq. 25), where
G = 4.28 years and Ne = 340 for the simulated population,
according to expressions given by Felsenstein (1971), and Fj are
the simulated temporal allele frequency shifts. The simulations
yielded Cj = 6.77, 8.56, 8.54, 9.01, 10.23, 11.57, 12.35, 13.12,
14.60 for j = 1–9. We note that the first value (6.77) for samples
drawn from consecutive cohorts, j = 1, is in good agreement
with the value (6.68) predicted using Jorde & Ryman’s (1995)
analytical approach. Thus, the computer simulations should
provide reasonably accurate corrections for the effects of overlapping generations in coastal cod populations. The estimation
is described in the main text.