Conservation Genetics 4: 249–264, 2003.
© 2003 Kluwer Academic Publishers. Printed in the Netherlands.
249
Effective population size and temporal genetic change in stream resident
brown trout (Salmo trutta, L.)
Stefan Palm1∗ , Linda Laikre1 , Per Erik Jorde1,2 & Nils Ryman1
1 Division of Population Genetics, Stockholm University,
S-10691 Stockholm, Sweden; 2 present addresses: Institute
of Marine Research, Department of Coastal Zone, Flødevigen Marine Research Station, N-4817 His, Norway, and
Division of Zoology, Department of Biology, University of Oslo, P.O. Box 1050 Blindern, N-0316 Oslo, Norway
(∗ Author for correspondence, e-mail: stefan.palm@popgen.su.se)
Received 25 February 2002; accepted 15 May 2002
Key words: allozymes, conservation, genetic drift, heterozygosity, monitoring, Ne , overlapping generations,
temporal method
Abstract
Temporal genetic data may be used for estimating effective population size (Ne ) and for addressing the ‘temporal
stability’ of population structure, two issues of central importance for conservation and management. In this paper
we assess the amount of spatio-temporal genetic variation at 17 di-allelic allozyme loci and estimate current
Ne in two populations of stream resident brown trout (Salmo trutta) using data collected over 20 years. The
amount of population divergence was found to be reasonably stable over the studied time period. There was
significant temporal heterogeneity within both populations, however, and Ne was estimated as 19 and 48 for
the two populations. Empirical estimates of the probability of detecting statistically significant allele frequency
differences between samples from the same population separated by different numbers of years were obtained.
This probability was found to be fairly small when comparing samples collected only a few years apart, even
for these particular populations that exhibit quite restricted effective sizes. We discuss some implications of the
present results for brown trout population genetics and conservation, and for the analysis of temporal genetic
change in populations with overlapping generations in general.
Introduction
Temporally replicated sampling has become
increasingly common in empirical genetic studies
of natural populations. One reason for this trend is
that temporal data can be used for estimating the
genetically effective population size (Ne ), a key
parameter in conservation and population biology
(e.g., Hedgecock et al. 1992; Miller and Kapuscinski
1997; Scribner et al. 1997; Lehmann et al. 1998; Funk
et al. 1999; Turner et al. 1999). The effective size
summarizes the relevant particulars of reproduction
into one comprehensive measure that quantifies the
rate at which a population is expected to lose genetic
variation and accumulate inbreeding over time.
Because of the large number of demographic factors
that influence this quantity, Ne is typically difficult to
estimate directly. The effective size may be estimated
indirectly, however, from measurements of temporal
change in allele frequencies (e.g., Nei and Tajima
1981; Waples 1989a); larger shifts are expected in
effectively small populations and vice versa.
Another reason for performing temporal genetic
sampling appears to reflect the concern that studies on
spatial genetic heterogeneity that are based on samples
collected on a single occasion only may provide a
biased picture of the amount of population differentiation (Allendorf and Phelps 1981; Jordan et al.
1992; Ryman 1997; Waples 1998). In salmonid fishes,
for example, several recent studies have included
temporal genetic data (e.g., Moran et al. 1995;
Hansen and Loeschke 1996; Moffet and Crozier 1996;
250
Stone et al. 1997; Estoup et al. 1998; Nielsen et
al. 1999; Tessier and Bernatchez 1999; Banks et
al. 2000; Carlsson and Nilsson 2000, 2001; Kanda
and Allendorf 2001). A frequent conclusion in these
studies is that the amount of temporal change within
populations is minor in comparison with the differences observed between populations. The overall
proportion of reported significant temporal changes
within populations is also typically small (but see, e.g.,
Jorde and Ryman 1996; Garant et al. 2000; Laikre et
al. 1998, 2002).
The scarcity of studies reporting significant
temporal genetic heterogeneity is somewhat surprising
considering that such variation is expected due to
genetic drift and other microevolutionary processes
(e.g., Waples 1989b). In particular, for organisms
with overlapping generations, such as salmonids,
theoretical work on temporal dynamics has shown
that larger allele frequency shifts may be observed
over short periods of time (e.g., intervals shorter
than a few generations) than for discrete generation populations of the same effective size (Waples
1990; Jorde and Ryman 1995; Ryman 1997). In
age-structured populations the individuals belong to
various cohorts (year-classes) that are expected to be
genetically different. This differentiation is due to
a limited number of parents producing each cohort,
and to the fact that those parents, in turn, frequently
represent only a restricted number of the age-classes
present in the population. As a consequence of the
reproductive pattern, populations with overlapping
generations typically display ’systematic’ short term
allele frequency fluctuations that occur in addition to
random genetic drift. For example, the amount of short
term change in the entire population may be greater
or smaller (depending on the demography) than the
amount of change expected from Ne alone (Jorde
and Ryman 1995). Similarly, allele frequency differences among consecutive cohorts are usually larger
than those of the total population over the same period
of time, and when samples for genetic analysis are
taken from one or a few age-classes only (e.g., juveniles or mature adults), the short term allele frequency
shifts observed may be poor indicators of those in the
population as a whole.
No finite populations are temporally stable except
in a relative sense. Nevertheless, the expression
‘temporal stability’ is commonly used to describe a
situation where the amount of genetic change within
a population appears so small that it may be safely
ignored in studies of spatial population structure.
Several authors have also suggested that their observations of such apparent temporal stability (i.e., lack
of statistical significances) in certain salmonid populations may reflect an Ne so large that only minor
allele frequency shifts occur (e.g., Jordan et al. 1992;
Hansen et al. 1993; Hansen and Loeschke 1996;
Tessier and Bernatchez 1999). An alternative reason
for not finding significant temporal genetic heterogeneity may be low statistical power for detecting
the allele frequency shifts actually occurring over the
observed period. In such cases, an observation of
‘temporal stability’ may provide little or no information on the effective size or on the true allele
frequency dynamics of the population. The matter of
power is quite complex, though, and depends on a
series of factors including effective population size,
sample size, and the time span separating the samples
(Waples 1989b). For species with overlapping generations the population demographic characteristics and
the age composition of the samples also play important
roles (Waples and Teel 1990; Jorde and Ryman 1995,
1996; Ryman 1997; Laikre et al. 1998). Clearly,
there is a need for studies providing estimates of
effective population size that also assess the probability of detecting temporal genetic change under
different ecological and sampling conditions.
In this paper we estimate the effective size of
two natural stream resident populations of brown
trout (Salmo trutta). This species has been subject
to extensive ecological and genetic analysis (e.g.,
Elliott 1994; Laikre 1999; and references therein), but
so far only few studies have attempted to estimate
Ne (Jorde and Ryman 1996; Laikre et al. 1998,
2002). The brown trout is typical for many species
having overlapping generations; i.e., only some of the
multiple age-classes participate in reproduction, and
the relative contribution of these mature age-classes to
the newborns vary. In addition, the species is iteroparous and individuals may reproduce more than once
during their lifetime.
Using temporal genetic data collected over a period
of nearly 20 years we estimate current Ne to be fairly
small for both of these populations (19 and 48). Estimates of the proportion of significant allele frequency
comparisons observed between samples separated by
different numbers of years are also provided, and
our case study illustrates empirically that extensive
sampling sometimes is needed to detect temporal
heterogeneity, also when the effective size is small.
251
Figure 1. The Haravattsån stream, central Sweden, and the two sampled localities (I and II). Small arrows indicate the direction of waterflow,
and numbers represent elevations (m). Letters A-C mark waterfalls that are referred to in the text. No brown trout were present in the water
system above fall A until 1979.
Materials and methods
The brown trout examined were collected within
the scope of an ongoing long-term genetic and
ecological survey of natural and introduced salmonid
populations in the County of Jämtland, central
Sweden (Jorde and Ryman 1996; Palm and Ryman
1999). The present material is from the Haravattsån
stream (mean annual flow c. 1.3 m3 /s) located in
the uppermost part of the River Indalsälven drainage
system that flows into the Baltic Sea (Figure 1). In
this stream natural brown trout are present below an
impassable waterfall (A in Figure 1), and the fish were
collected from two sections located about 2 km apart.
The two stream sections are of similar length (150–
250 m) but represent contrasting habitats. The uppermost section (Locality I) is located directly below the
impassable waterfall A and is delimited downstream
by a smaller waterfall. In Locality I the stream consists
of some deep pools (maximum depth 6 m) interrupted
by shallow passages. In contrast, Locality II represents
a short subset of an approx. 3 km shallow part of the
252
stream (depth usually below 0.5 m) that lacks apparent
barriers for fish migration (between falls B and C;
Figure 1). There are significant growth differences
between the trout of the two locations, the growth
being faster at Locality I (e.g., the mean total length at
age 6+ is 24.3 cm in Locality I as compared to 17.2 cm
in Locality II; unpublished data).
Materials: Sampling in the Haravattsån stream was
initiated in 1980. About 100 (mainly adult) trout
have been collected annually from each locality, with
the exception of a few years in the early phase
of the project when no sampling took place. Fish
were caught by angling in July or August. The
present analysis is based on collections through 1999.
For each fish weight, total length, and sex was
recorded. Otoliths for age determination (Filipsson
1967; Williams and Bedford 1974) and subsequent
cohort assignment were collected, as well as tissue
samples for protein electrophoresis (white skeletal
muscle, eye, and liver; see Jorde and Ryman (1996)
for details). In recent years the stage of maturation
has also been recorded (breeding the year of collection or not; recorded since 1990 and 1991 in Locality
I and II, respectively). The collection in a particular
year always comprised at least five age-classes, 2–3
of which typically constituted about 75% of the catch.
For the statistical evaluations all individuals belonging
to a specific cohort (within locality) were lumped;
thus, each cohort-locality combination comprised fish
of various age collected in different years.
For Locality I only fish born in 1987 or earlier were
used (n = 636), whereas all cohorts available from
Locality II were included (n = 1392), and the reason
for this difference is as follows. Until the late 1970s
Arctic char (Salvelinus alpinus) was the only fish
species present above the waterfall A (Figure 1), but
in 1979 brown trout was introduced in the uppermost
part of the water system as part of a transplantation
experiment (Palm and Ryman 1999). Our interest here
refers exclusively to the characteristics of the natural
populations at Localities I and II before any potential
effect of immigration has occurred. The introduced
fish were genetically marked and distinct from those at
Locations I and II at several allozyme loci; identification of immigrants and first generation hybrids could
be achieved with a high degree of precision. To date,
there is no evidence of exogenous genes in Locality II,
and all the fish collected from this locality through
1999 was therefore included in the present analysis
(Table 1).
With respect to Locality I there is strong evidence
of substantial immigration of introduced fish (and their
progeny) and subsequent hybridization, particularly
during recent years. Because the influx of exogenous
genes into this locality may provide a biased picture
of the genetic composition and temporal dynamics
of the ‘original’ local population, the 636 individuals
from Locality I included here represent fish obtained
through i) eliminating cohorts born after 1987 (potentially including second generation hybrids that may
be difficult to identify), and ii) removing from the
remaining data set fish that could be identified as
immigrants or first generation hybrids on the basis
of their genotype. The details of the introgression
process will be reported separately. With respect to
the present data set, however, the observed distribution of multilocus genotypes indicates that the probability that the number of unidentified exogenous
trout (including hybrids) among the 636 ones from
Locality I exceeds four is less than 3%. For the
1392 fish from Locality II a similar assessment yields
a probability of this material including more than
six immigrants of less than 5%. Thus, the possible
existence of unidentified descendants from the introduced stocks should have little effect on the present
analyses.
Genetic and statistic analyses: Screening of allozymes
was performed by conventional horizontal starch gel
electrophoresis of known polymorphic loci (Allendorf
et al. 1977; Guyomard and Krieg 1983; Taggart
and Ferguson 1984; Jorde et al. 1991; Jorde 1994).
We follow the nomenclature proposed by Shaklee
et al. (1990) for designation of loci and alleles
with modifications as suggested by the ‘TroutConcert
Specialist Group’ (www.qub.ac.uk/bb/prodohl/ TroutConcert/TroutConcert.htm).
The following 17 loci were found to be polymorphic (previous locus designations in papers from
our group in brackets; alleles in parenthesis, the
∗ 100 allele representing the generally most common
one): sAAT-4∗ [AAT-6] (∗ 100, ∗ 50); CK-A1∗ [CPK-1]
(∗ 115, ∗ 100); DIA-1∗ [DIA] (∗ 100, ∗ 95); bGALA-2∗
(∗ 100, ∗ 95); bGLUA∗ [BGA] (∗ 150, ∗ 100); G3PDH2∗ [AGP-2] (∗ 100, ∗ 50); sIDDH-1∗ [SDH-1] (∗ 100,
∗ -50); sIDHP-1∗ [IDH-2] (∗ 160, ∗ 100); LDH-A1∗
[LDH-1] (∗ 100, ∗ QO); LDH-C1∗ [LDH-5] (∗ 105;
∗ 100); aMAN∗ (∗ 100, ∗ 70); sMDH-2∗ [MDH-2]
(∗ 125, ∗ 100); sMDH-3,4∗ [MDH-3,4] (∗ 125, ∗ 100,
∗ 80); ME∗ [MEL] (∗ 120, ∗ 100); MPI-2∗ [PMI] (∗ 105,
∗ 100); PEPLT∗ (∗ 100, ∗ 70). Several of these poly-
253
Table 1. Basic genetic data for two stream resident brown trout populations: sample sizes, allele frequency ranges (over sampling years and
cohorts) for the generally most common allele (∗ 100) at 17 di-allelic allozyme loci, FI S expected heterozygosity (H), and levels of significance
from exact tests for Hardy-Weinberg conformance (significance level of FI S ) and for temporal allele frequency homogeneity (significance level
of allele frequency ranges). FST (Weir and Cockerham 1984) quantifies the divergence between populations (FI S and FST correspond to FI T
and FLT in the hierarchical designs in Table 2). Allele frequency ranges were computed from samples with a minimum of 20 fish, whereas the
exact significance tests for allele frequency homogeneity include all samples. The ‘total’ significances given at the bottom of each range-column
(all P < 0.001∗∗∗ ) were obtained by combining single locus P-values using Fisher’s method. All monomorphic loci in Locality I (i.e., those
without a range) are fixed for the ∗ 100-allele
Locus
sAAT-4∗
CK-A1∗
DIA-1∗
bGALA-2∗
bGLUA∗
G3PDH-2∗
sIDDH-1∗
sIDHP-1∗
LDH-A1∗†
LDH-C1∗
aMAN∗
sMDH-2∗
sMDH-3∗†
sMDH-4∗†
ME∗
MPI-2∗
PEPLT∗
Total
H (17 loci)
H (74 loci)
Locality I
No. FI S
of
fish
No.
Allele
of
frequency
years range (years)
Locality II
No.
Allele
No.
FI S
of
frequency
of
cohorts range (cohorts) fish
No.
Allele
of
frequency
years range (years)
427 0.04
543 –0.03
319
319 0.16∗
319 0.04
636
416 0.09
319
636
636
319
636 –0.02
319
636
319 0.02
319 0.09
319 –0.02
8
9
7
7
7
10
8
7
10
10
7
10
7
10
7
7
7
11
12
8
8
8
14
10
8
14
14
8
14
8
14
8
8
8
13
14
12
12
12
14
14
12
14
14
12
14
12
14
12
12
12
0.024∗
0.59–0.74
0.78–0.91∗∗
0.91–0.98
0.90–0.95
0.90–1.00∗∗∗
0.48–0.66
0.95–1.00∗∗∗
0.52–0.61
0.96–0.98
0.89–0.97
P < 0.001∗∗∗
0.61–0.74
0.68–0.96∗∗∗
0.76–0.98∗∗∗
0.90–0.97
0.90–1.00∗∗∗
0.39–1.00∗∗∗
0.94–1.00∗∗∗
0.48–0.69∗
0.91–0.99
0.82–0.97∗∗
P < 0.001∗∗∗
1249
1392
1178
1174
1175
1392
1385
1178
1392
1392
1176
1392
1179
1392
1179
1176
1179
–0.03
0.13∗∗∗
–0.01
–0.02
0.03
0.09∗∗
–0.01
–0.04
–0.01
0
0.01
–0.05
–0.03
0.00
–0.003
0.132
0.030
FST
No.
Allele
(between
of
frequency
localities)
cohorts range (cohorts)
0.71–0.85∗∗
0.94–0.99
0.97–1.00
0.55–0.66
0.68–0.83∗
0.73–0.92∗∗∗
0.59–0.77∗∗
0.60–0.78∗
0.74–0.89
0.86–0.95
0.99–1.00
0.60–0.77∗∗
0.88–0.94
0.76–0.87∗
0.77–0.86
0.95–1.00
0.82–0.95∗∗
20
22
18
18
18
22
22
18
22
22
18
22
18
22
18
18
18
P < 0.001∗∗∗
0.68–0.91∗∗∗
0.94–0.99
0.96–1.00
0.53–0.75∗∗
0.61–0.83∗∗
0.64–0.97∗∗∗
0.57–0.79∗∗∗
0.56–0.86∗∗∗
0.67–1.00
0.83–0.97∗∗∗
0.99–1.00
0.52–0.82∗∗
0.86–0.97∗
0.74–0.89∗∗
0.74–0.88∗
0.95–1.00
0.78–0.96∗∗∗
0.028∗∗∗
0.156∗∗∗
0.007∗∗
0.212∗∗∗
0.084∗∗∗
0.110∗∗∗
0.171∗∗∗
0.233∗∗∗
0.082∗∗∗
0.063∗∗∗
–0.001
0.207∗∗∗
0.056∗∗∗
0.150∗∗∗
0.147∗∗∗
–0.001
0.012∗∗∗
P < 0.001∗∗∗
0.133∗∗∗
0.254
0.058
∗ P < 0.05; ∗∗ P < 0.01; ∗∗∗ P < 0.001.
† Locus scored as dominant; exact tests performed on phenotypic frequencies; F cannot be computed.
IS
morphisms were detected during the present study
(e.g., Jorde et al. 1991; Jorde 1994) and not all were
screened before 1988. Thus, the number of genotyped
individuals varies considerably between loci (Table 1).
In addition to the above loci, previous electrophoretic
screening revealed 57 putative loci that appear monomorphic or nearly so in the present populations (Jorde
and Ryman 1996).
Three loci (LDH-A1∗ and sMDH-3,4∗ ) were
scored as ‘dominant’; allele frequencies at these loci
were estimated from the frequency of the ‘recessive’
phenotype (assuming Hardy-Weinberg proportions)
following Jorde et al. (1999). The polymorphism
at LDH-A1∗ is due to a null allele which makes it
very difficult to distinguish more than two banding
patterns (Allendorf et al. 1984). sMDH-3,4∗ represents
a pair of isoloci (both have ∗ 100 alleles with identical
electrophoretic mobility) where we usually score the
variant ∗ 80 and ∗ 125 alleles in muscle and eye tissue,
Table 2. F-statistics for temporal and spatial genetic variation in
brown trout. The computations were performed through analyses
of variance of allele frequencies (e.g., Weir and Cockerham
1984) including co-dominant loci only. Levels of significance
were evaluated through permutations. Only those cohorts were
included where a minimum of ten fish had been scored for all the
co-dominant loci. Note that FLT and FI T correspond to FST and
FI S in the non-hierarchical analyses in Table 1
Fixation index
Analysis including
Both
localities
Between localities (FLT )
Between cohorts within
locality (FCL )
Within individuals within
cohorts (FI C )
Within individuals within
total (FI T )
∗ P < 0.05; ∗∗∗ P < 0.001.
0.144∗∗∗
0.014∗∗∗
–0.014
0.145∗∗∗
Locality I
Locality II
0.019∗∗∗
0.014∗∗∗
0.004
–0.016∗
0.023
–0.002
254
respectively. We cannot separate the banding patterns
for individuals carrying different number of ‘doses’
of these variant alleles, and assumed that this polymorphism was due to two separate loci where the slow
(∗ 80) and fast (∗ 125) variant alleles are both dominant
to the common (∗ 100) allele (but co-dominant to each
other). Hence, the ∗ 80 and ∗ 125 alleles have been
arbitrarily designated to sMDH-3∗ and sMDH-4∗ ,
respectively (Jorde 1994).
The statistical significance of allele frequency
differences and deviations from Hardy-Weinberg
proportions were evaluated by chi-square tests
(Ryman and Jorde 2001) and exact tests using
GENEPOP 3.3 (Raymond and Rousset 1995).
F-statistics (Weir and Cockerham 1984; Nei 1987)
quantifying spatial and temporal genetic heterogeneity
and their significances were estimated in hierarchical analyses using the softwares ARLEQUIN 2.001
(Schneider et al. 2000) and FSTAT 2.9.3 (Goudet
1995, 2001). In these hierarchical analyses we only
used data from the 14 co-dominant loci and the cohorts
for which all loci had been scored.
Estimation of Ne : Variance effective population size
was assessed using the so-called temporal method
(e.g., Nei and Tajima 1981; Waples 1989a; Williamson and Slatkin 1999) following the approach
of Jorde and Ryman (1995, 1996). This approach
was developed specifically for overlapping generations, and implies that Ne (per generation; not
to be confused with Nb , the effective number of
breeders per year; e.g., Waples 1990) is estimated
from temporal shifts of allele frequencies between
consecutive cohorts under the assumption that these
shifts represent random genetic drift and sampling
error only. All fish were sampled destructively and
not returned to the population, but we evaluated the
allele frequency shifts between consecutive cohorts
under the so-called sampling plan I (Nei and Tajima
1981; Waples 1989a) assuming that removal of individuals from one cohort does not affect the allele
frequency of the following one, and that the number
of newborns (N1 ) in each cohort is so large that the
term 1/N1 can be ignored. As discussed by Jorde and
Ryman (1996) these assumptions seem reasonable for
a species where the first age-class does not contain
mature individuals, and where the fecundity is high
and survival rates are low.
Pollak’s (1983) Fk was used to quantify the
observed allele frequency shifts, and this quantity was
corrected for sampling (Fk ) following Pollak (1983,
eqn. 20). A slightly modified version of Fk was
applied that is expected to be less biased when sample
sizes are small (i.e., when number of individuals
<50; Jorde and Ryman, unpublished). However, the
difference between Ne estimates generated by the two
different ways of computing Fk was small for the
present material. For the three dominant loci, Fk was
calculated using the equations provided by Jorde et al.
(1999).
Allele frequencies close to 0 or 1 may result
in biased Ne estimates (Waples 1989a; Turner et
al. 2001). Thus, to avoid unnecessary bias, at any
particular locus we only included allele frequency
shifts between pairs of consecutive cohorts where the
average frequency of the variant allele was 0.025 or
higher (all loci are di-allelic; Table 1). For similar
reasons, only those pairs of consecutive cohorts were
used where the harmonic mean sample size (number
of fish) was at least 10 or 20 at co-dominant and
dominant loci, respectively (Jorde et al. 1999). All in
all, this resulted in 64 and 243 usable Fk values for
Locality I and II, respectively.
When generations overlap (as in the brown trout)
the amount of temporal shift of allele frequencies
depends not only on Ne but also on the demographic
characteristics of the population. Allele frequency
changes between consecutive cohorts are expected to
be larger than for the population as a whole, and life
table data are required for calculating a correction
factor (C) that accounts for this phenomenon and for
assessing the generation interval (G; Jorde and Ryman
1995, 1996).
Age specific survival rates (li ) were estimated from
the observed number of trout (both sexes) in each ageclass using the Chapman-Robson method (Robson
and Chapman 1961; Youngs and Robson 1978). This
method takes into account that young age-classes may
be underrepresented in the catch; it is assumed that
the probability of survival from one year to another
is the same at all ages (type II mortality; e.g., Roff
1992). Many fishes, including the brown trout, are
characterized by a very high mortality during the
earliest life stages, and assuming a type II mortality
may therefore appear inappropriate. In the present
case, however, our life tables are based on an annual
‘enumeration’ that takes place after the period of high
mortality that is typical for the alevine and fry stages
and when the mortality starts to approach a constant
rate (Elliott 1993). Further, as was also observed on
brown trout in neighboring lakes (Jorde and Ryman
1996; their Figure 3), our present age distributions
255
Table 3. Age-specific estimates of li (survival rate), bi (birth rate), and pi (probability that a gene in an individual was
inherited from a parent in age-class i) for two stream resident brown trout populations. The birth rates, bi (m) and bi
(f), are for males and females, respectively, and their average were used when calculating pi . C is a correction factor for
overlapping generations and G an estimate of the generation interval calculated from li and pi . See text for details
Age
0+
1+
2+
3+
4+
5+
6+
7+
8+
9+
10+
11+
C
G
Age-class (i)
1
2
3
4
5
6
7
8
9
10
11
12
Locality I
Locality II
li
bi (m)
bi (f)
pi
li
bi (m)
bi (f)
pi
1.0000
0.3672
0.1349
0.0495
0.0182
0.0067
0.0025
0.0009
0.0003
0.0001
0.0000
0.0000
0
0
0
1.8
14.5
40.6
77.5
108.3
170.2
170.2
170.2
170.2
0
0
0
0
5.1
51.6
126.8
166.4
186.5
220.7
220.7
220.7
0
0
0
0.044
0.178
0.308
0.251
0.124
0.059
0.024
0.009
0.003
1.0000
0.3773
0.1424
0.0537
0.0203
0.0076
0.0029
0.0011
0.0004
0.0002
0.0001
0.0000
0
0
0
2.1
14.6
31.3
60.3
83.7
130.7
144.9
144.9
144.9
0
0
0
0.7
13.2
50.0
60.7
78.4
78.4
78.4
78.4
78.4
0
0
0
0.076
0.281
0.311
0.174
0.088
0.043
0.017
0.007
0.002
14.4
6.6
for older (mature) age-classes show a good fit to
that expected under a type II mortality (data not
shown).
Age and sex specific birth rates (bi ) were assessed
from the observed proportions of mature fish in
various age-classes weighted by body size (weight)
after normalizing the bi values to provide a constant
population size (li bi = 1). Finally, the li and bi
values were used for calculating pi = li bi , the estimated probability that a gene in an individual was
inherited from a parent of age i, and the factors C and
G (using the expressions 5 and 10 of Jorde and Ryman
(1996), respectively).
Our bi estimates (Table 3) are necessarily associated with a large degree of uncertainty because
the quantity of interest, i.e., the average number of
‘newborns’ produced by a fish of a particular age,
has not been measured directly. Fortunately, however,
this uncertainty does not appear to pose a major
problem for estimation of Ne in the present populations. Without going into details, it is the product
pi = li bi (rather than li or bi by themselves) that is
of interest when assessing the factors C and G used
for estimating Ne . Further, for the present populations which are characterized by a low annual survival
rate (less than 0.4; Table 3), the estimates of Ne are
quite robust to uncertainties regarding bi . Extensive
12.4
6.2
sensitivity analyses (not presented) have shown that
with i) the present approximate li values, ii) a maturation age of 3+ to 4+, and iii) the constraints of a
constant population size (i.e., li bi = 1), the estimates
of Ne remain strikingly stable for a wide range of bi
values. This observation is in line with previous findings by Jorde and Ryman (1995, 1996), suggesting
that the present method for estimating Ne appears quite
robust to moderate uncertainties in the demographic
parameter estimates.
Confidence intervals for the Ne estimates were
obtained using the method suggested by Waples
(1989a) under the assumption that Fk follows a χ 2
distribution with one degree of freedom (di-allelic
loci). This approach resulted in confidence intervals
that were almost identical to those obtained using a
Normal approximation (cf. Turner et al. 2001).
Results
Our results are consistent with those expected when
sampling from two genetically distinct populations of
restricted effective size where generations overlap. In
such a situation we expect to find i) an overall allele
frequency heterogeneity among populations, ii) allele
frequency differences between cohorts within each
256
population, and iii) a slight excess of heterozygotes
within cohorts of the same population due to the
restricted number of parents producing each cohort
(e.g., Robertson 1965; Pudovkin et al. 1996). In
contrast, the total (pooled) material may display
a heterozygote excess, deficiency, or no deviation
from Hardy-Weinberg proportions. The difficulty in
predicting the direction and degree of deviation from
Hardy-Weinberg proportions in the total material is
because the heterozygote excess within cohorts may
be counterbalanced by a heterozygote deficiency (a
Wahlund effect) that is dependent on the magnitude of
the allele frequency differences between cohorts and
populations (cf. Christiansen 1988).
The observed allele frequencies are presented in
Table 1. Clearly, there are genetic differences between
Locality I and II; a majority of the loci display significant allele frequency differences and the overall FST =
0.13 must be considered fairly large for two neighboring populations with a potential for gene flow in
at least one direction. Such marked discontinuities
are common in the brown trout and other salmonids,
however (e.g., Ryman 1983; Allendorf and Leary
1988; Ferguson 1989). The difference between the
localities is fairly stable over time, the FST estimates
for separate years ranging from 0.10 to 0.19 (all P <
0.001; data not shown).
There is an obvious difference with respect to
the amount of genetic variability within the two
populations. The number of variable loci is lower in
Locality I (10 vs. 17), as is the average heterozygosity
(H [74 loci] = 0.030 and 0.058 in Locality I and II,
respectively; Wilcoxon’s signed-ranks test for paired
observations yields P = 0.044; cf. Nei 1987; Luikart
et al. 1998). Within Locality I there is a slight tendency towards an overall heterozygote deficiency across
loci (FI S > 0), whereas no such trend can be seen in
Locality II (Table 1).
There is marked temporal genetic variation within
both populations as revealed by the significant allele
frequency heterogeneities among both sampling years
and cohorts (Table 1). In both populations the
magnitude of these differences are larger among
cohorts than among sampling years, as expected when
each year comprises fish of various age representing
different cohorts. (In Table 1 the tests for overall
heterogeneity were obtained by Fisher’s method; the
corresponding P-values are even smaller using the
chi-square summation approach, but this difference is
unimportant in the present context of obvious heterogeneity; cf. Ryman and Jorde 2001.)
The amount of spatial and temporal variation in the
total material (T) was quantified by F-statistics using
the hierarchy locality (L), cohort (C) within locality,
and individual (I) within cohort (Table 2). Most of
the overall allele frequency variation is due to population divergence, the spatial component (FLT ) being
about ten times larger than the variation among cohorts
within localities (FCL ). The minor difference between
the estimates of population differentiation in Tables 1
and 2 (FST = 0.133 vs. FLT = 0.144) is due to computational differences (non-hierarchical vs. hierarchical
design) and to the fact that Table 2 is based exclusively
on co-dominant loci and a somewhat smaller number
of fish.
With respect to FI C , which quantifies the deviation
from Hardy-Weinberg expectations within cohorts, we
observe a weak, but significant, heterozygote excess
in Locality II (FI C < 0; Table 2), whereas FI C is
not significantly different from zero in Locality I.
The number of fish and polymorphic loci is considerably larger for Locality II than for Locality I
(Table 1), however, and the overall result indicates a slight heterozygote excess within cohorts, as
expected when the number of parents of a cohort is
restricted.
When considering the total material, the marked
overall heterozygote deficiency (FI T 0) appears
primarily to be explained by a Wahlund effect
reflecting the fairly large allele frequency differences
between the two populations. In contrast, FI T is close
to zero within each locality (Table 2), most likely
because of the comparatively smaller differentiation
among cohorts that results in a weaker Wahlund effect
balancing the heterozygote excess within cohorts. For
Locality I the hierarchical analysis yields a nonsignificant FI T , whereas the corresponding (total) FI S
in the non-hierarchical analysis (Table 1) is marginally significant. We note, however, that the test in
Table 1 was produced using the multisample score
test of GENEPOP, whereas applying a corresponding
permutation test in FSTAT results in non-significance
(P ≈ 0.10).
For comparison with the Weir-Cockerham estimates presented in Table 2, we also computed Fstatistics using the gene diversity approach of Nei
(e.g., 1987). For the present material, the two methods
result in similar estimates (data not shown). The only
major difference was found for FLT which was 0.144
and 0.091 for Weir-Cockerham and Nei, respectively.
This difference is due primarily to the Nei estimate
being dependent on the number of populations, and
257
Table 4. Average temporal allele frequency shifts between
consecutive cohorts (F¯k and F¯k ) and estimates of effective
population size (N̂e ) with 95% confidence intervals (C.I.)
Number of F-values
F¯k
F¯ k
N̂e
C.I.
Locality I
Locality II
64
0.0904
0.0563
19
11–35
243
0.0422
0.0208
48
34–71
correcting for this dependence (Nei 1987) results in
an FLT = 0.167 that is more close to that of WeirCockerham.
We also searched for genetic differences between
fish belonging to the same cohort (born in the same
year) sampled in different years, potentially indicating, for example, immigration or the operation of
selection. No evidence of such heterogeneity within
cohorts was found. Within each combination of
locality, cohort, and locus exact contingency tests for
allele (and genotypic) frequency homogeneity among
sampling years were performed; out of a large number
of tests less than five percent were significant on the
5% level, and no tendency for these significances to
represent particular loci or cohorts could be seen.
Effective population size: The li , bi , and pi estimates,
as well as the quantities C and G, are quite similar for
the two locations (Table 3). There is a tendency for
the fish in Locality II to start reproducing somewhat
earlier, which is also reflected in a shorter generation
interval, but these differences are minor.
Using the average standardized variances in allele
frequency shifts between consecutive cohorts (F¯k ;
Table 4) and the observed values of C and G, the
effective population size was estimated as 19 and 48
for Locality I and II, respectively. The 95% confidence
intervals show only marginal overlap, and a randomization test for equal means of Fk values in the two
populations yields a highly significant result (P =
0.002; e.g., Sokal and Rohlf 1981), indicating a real
difference in effective size.
Since the present data set represents a series of
consecutive cohorts, it was possible to check for variation of effective population size over the study period.
Using the same type of randomization approach as
when testing for a population difference, we addressed
the hypothesis that average Fk was the same for
all pairs of consecutive cohorts (within locality).
The temporal heterogeneity in Fk was significant in
Locality II (P = 0.003), but not in Locality I (where the
number of cohorts and polymorphic loci is smaller).
The present kind of Ne estimates are necessarily associated with a large sampling error, and it is difficult to
see a trend in this variation when only considering the
point estimates for the separate pairs of consecutive
cohorts. Smoothing by means of moving averages,
however, indicates that Ne of Locality II was smaller in
the early and late years of the period than in between
(Figure 2).
Detecting temporal change: The probability of
detecting temporal change of allele frequencies within
populations depends on several factors, as illustrated by the observed proportion of significant tests
between pairs of sampling years and cohorts separated by different number of years (Figure 3). First,
the proportion of significances is generally larger
in Locality I, in line with the smaller Ne estimate
of this population. Second, it is increasingly easier
to detect temporal heterogeneity as the time period
separating the samples grows larger (cf. Waples
1989b). Third, summation of chi-square statistics over
multiple loci increases the probability of obtaining
significant sample comparisons (cf. Ryman and Jorde
2001). Finally, when considering comparisons over
‘short’ periods the temporal heterogeneity is more
accentuated between cohorts than between sampling
years (consisting of a mixture of multiple cohorts;
cf. Jorde and Ryman 1995). In the present data
set this tendency of a higher proportion of significances between cohorts than between years is most
pronounced for samples separated by about five years
or less. We note that this time period corresponds
roughly to the estimates of generation time (G = 6.2 –
6.6 years), but the relevance of this observation is
presently not clear.
Discussion
The present empirical case study has focused on
spatio-temporal genetic variation in stream resident
brown trout. In brief, we have presented evidence that
our samples are from two distinct populations inhabiting the same stream, estimated Ne from temporal
shifts of allele frequencies, and assessed the probability of detecting temporal change over different
periods of time. For the purpose of the present
258
Figure 2. Point estimates of effective size (N̂e ) for all pairs of consecutive cohorts ( and for Locality I and II, respectively), and the
corresponding (harmonic) mean N̂e (open symbols) obtained from moving averages for Fk over five consecutive cohorts (i.e., four cohort
pairs). ‘Cohort’ on the x-axis represents the first cohort used for each Ne estimate. Stippled lines indicate the total estimate for each population
(cf. Table 4). Note the broken y-axis and that large Ne point estimates are given as numbers (∞ = infinity).
presentation the discussion here focuses primarily on
issues relevant to brown trout population genetics and
conservation, and on some aspects relating to the interpretation of temporal genetic data from populations
with overlapping generations.
Brown trout genetics: We have observed a ‘stable’
genetic population structure, where the spatial
component of variation is significantly larger than
that of the temporal one within the populations. This
observation is similar to what has been found in
several other studies of salmonid fishes (e.g., Jordan
et al. 1992; Moran et al. 1995; Jorde and Ryman
1996; Moffet and Crozier 1996; Stone et al. 1997;
Carlsson et al. 1999; Nielsen et al. 1999; Tessier and
Bernatchez 1999; Kanda and Allendorf 2001; Laikre
et al. 2002). With respect to our observations on the
amount of temporal genetic change, however, there are
few empirical results to compare with.
The effective size estimates of the present populations are 19 and 48 for Locality I and II, respectively.
We are aware of only four other brown trout populations where Ne has been estimated. Those four populations are located within a 10 km distance from the
present stream resident ones and refer to lake dwelling
trout. The Ne estimates were obtained using the same
method and set of loci as in the present study, and
ranged between about 50 and 500 (Jorde and Ryman
1996). In addition, female effective size (Nef ) of two
populations has been assessed from temporal variation
of mtDNA haplotype frequencies (Laikre et al. 1998,
2002). For one of those populations total effective size
(Ne ) had also been estimated in the study by Jorde and
Ryman (1996), and it was found that the Nef estimate
was about half of that of Ne (Laikre et al. 1998). In the
other study of mtDNA variation the estimate of female
effective size represented a (harmonic) mean for 13
anadromous ‘sea trout’ populations at the Island of
Gotland in the Baltic Sea, and assuming that the total
effective size approximates twice that of the female
segment in these populations also, Ne would be in the
order of 50–70 (Laikre et al. 2002).
The population in Locality I (N̂e = 19) displays a
significantly smaller level of genetic variation (H =
0.030) than the effectively larger one at Locality II
(N̂e = 48; H = 0.058), as expected for isolated populations of different effective size. This empirical observation contrasts with the results of previous studies,
however. In particular, Jorde and Ryman (1996) found
the levels of heterozygosity in their four populations
to be strikingly similar (H in the range 0.052–0.061)
in spite of the fairly wide range of the Ne estimates
(50–500). Those authors suggested that the apparent
lack of correlation between N̂e and H might be due to
local populations being connected by naturally occurring gene flow of a magnitude that is small enough
to permit differentiation but large enough to prevent
excessive loss of genetic variation.
259
Figure 3. Proportion of chi-square tests yielding statistical significance (P < 0.05) in single locus pairwise allele frequency comparisons between sampling years () and cohorts () that are separated by different number of years. Only co-dominant loci and
samples with a minimum of 20 fish were used. The open symbols
represent the result when combining the information for multiple
loci (summation of chi-square for the eight and eleven most polymorphic loci in Locality I and II, respectively). The right-most
symbols indicate the overall average for each type of test. Total
number of single-locus tests are 80 and 1005 (years) and 175 and
1736 (cohorts) in Locality I and II, respectively; the corresponding
number of ‘multilocus tests’ are 6 and 66 (years) and 10 and
105 (cohorts). The small number of tests for Locality I is due to
the considerably smaller number of samples and polymorphic loci
available for this locality.
The estimates of Ne and H obtained in the present
study are consistent with such an explanation. First,
the population at Locality I is the only one (of the
six in this area for which estimates of Ne and H
are available) with an apparent potential for restricted
immigration from neighboring populations due to the
waterfall located immediately downstream of this site.
Second, the heterozygosity at the apparently less
isolated Locality II is remarkably similar to that of the
four lake populations, in spite of its relatively small Ne
estimate. The notion that gene flow constitutes a major
factor for the preservation of genetic variability in the
brown trout is also supported indirectly by observations from other studies. Most or all of the populations
that have been reported to display a notably low degree
of genetic variation refer to situations where immigration appears restricted, i.e., the population is either
physically isolated or located in the uppermost part
of the drainage (Garcia-Marin et al. 1991; Marshall
et al. 1992; Riffel et al. 1995; Prodöhl et al. 1997;
Carlsson and Nilsson 2001). It must be noted, though,
that none of those reports of low heterozygosity have
been accompanied by effective size estimates.
The results suggest that the samples from Locality
II are drawn from a single, effectively small, population, and it is not clear how to interpret these findings
with respect to the population structure in this lower
part of the Haravattsån stream. This site represents
a subset of an about 3 km long physically homogeneous section of the stream without apparent barriers to
migration and where brown trout is abundant (between
the falls B and C; Figure 1). The relatively small Ne
estimate may indicate that we have sampled only one
of several populations inhabiting different sections of
this part of the stream, but additional sampling above
and below Locality II is necessary for addressing this
issue.
The observation that the two stream resident
populations examined here represent the two smallest
estimates of Ne reported so far is interesting. It must
be noted, though, that at Locality II there is a significant variation of Ne over the time period examined (20
consecutive cohorts), and a shorter study could easily
have resulted in a larger estimate (Figure 2). Further,
because average Ne over time tends to approach a
harmonic rather than an arithmetic mean, estimates
of Ne are usually expected to decrease as longer time
scales are considered (e.g., Crow and Kimura 1970;
Vucetich and Waite 1998). Previous estimates are
based on fewer consecutive cohorts. The tendency of a
difference between lake and stream resident trout may
thus be spurious, and additional studies are required
to clarify whether or not this observation reflects a
general difference between life history forms.
Considerable interest in conservation and evolutionary biology is presently focused on the ratio Ne /N,
where N represents the ‘total’ population size (e.g.,
Frankham 1995; Vucetich and Waite 1998; Rieman
and Allendorf 2001; Kalinowski and Waples 2002).
A major reason for this interest is that information
on Ne /N might facilitate rough assessment of Ne from
260
census data alone. We have no information on the
total number of fish (N) at the sampled locations,
which precludes direct estimation of Ne /N ratios for
the present populations. However, we have sampled
(destructively, without replacement) about 100 adult
fish per year from each population without seeing any
indications of declining population sizes. Thus, if N
is taken as the total number of adults existing at a
given point of time, it is clear that Ne /N should be
smaller than 0.2 and 0.5 for Locality I and II, respectively, although our data do not allow inference on how
much smaller these ratios might be or whether they are
different for the two populations or not.
Finally, our present data lend further support to
the idea that natural brown trout populations are
commonly of a quite restricted effective size and that
gene flow plays a central role for the retention of
genetic variation (cf. Jorde and Ryman 1996; Laikre
et al. 1998, 2002). These observations reinforce the
need to focus conservation and management efforts on
the maintenance of population systems and migratory
routes rather than on particular local populations
alone.
Temporal genetic change and Ne : Most studies on
genetic variation in natural populations are based on
samples collected at one or a few occasions only,
and our data can be used to examine empirically to
what extent the results from a less exhaustive sampling
would have differed from the present ones. A typical
funding period, for example, only permits sampling
over two or three consecutive years.
With respect to the spatial aspect of population
structure, the divergence between Locality I and II is
so large that it seems unlikely that it would have gone
unnoticed even with only a single year of sampling. In
contrast, it is not as obvious what conclusions would
have been drawn regarding the amount of temporal
change within populations using a less exhaustive
sampling strategy.
It is clear that both populations have changed
genetically over time and that the temporal shifts are
substantial, i.e., they are large enough to correspond
to effective sizes that in most situations would be
considered quite restricted. It is also clear from the
moving averages depicted in Figure 2 that reasonably
accurate Ne estimates could have been obtained from a
considerably smaller number of cohorts than used for
our present overall estimates (Table 4). When considering Figure 2, however, it is important to realize
that each moving average represents genetic data for
five consecutive cohorts. The average time we spent
on collecting all the fish of a particular cohort was
5.8 years, whereas it took us about 4 years to obtain
90% of those individuals. Similarly, sampling over a
minimum of 6 consecutive years was required to get
the majority of the genetic data behind each moving
average in Figure 2.
In situations where a restricted number of samples
are taken only one or a few years apart, the probability
of detecting the existence of temporal heterogeneity
(i.e., of detecting that the populations are not ‘very
large’) may be fairly small (Figure 3). At Locality II,
for example, the probability of detecting a single
locus allele frequency shift between sampling years
that are 1–2 years apart is only about 10%, and the
corresponding probability for cohorts is about 20%
(Figure 3, lower panel). The power increases when
combining the information from multiple loci, but the
probability of obtaining a significance (P < 0.05) is
still quite modest (about 40% and 60%, respectively),
even when the number of loci is relatively large (here
11 di-allelic ones).
The probability of detecting temporal heterogeneity increases when comparing samples that are
separated by more than a few years, and particularly so at Locality I. The increase of power over
time is consistent with theoretical expectations (as
discussed by Waples 1989b for populations with nonoverlapping generations), but the rate of increase is
quite slow at each particular locus if the effective size
is not very small (as in Locality I). Thus, even allele
frequency changes over a time period of ten years or
more may go undetected in a population with an Ne
of about 50 unless a ‘reasonable’ number of loci is
examined (Figure 3). It should be stressed, though,
that our observations are strictly empirical, and that
a more general treatment of the issues of statistical
power for detecting temporal genetic heterogeneity
when generations overlap appears warranted.
Robustness to assumptions: Our conclusions are based
on a number of assumptions, a few of which may be
violated to some extent. Much of the analysis, for
example, is based on assignment of individuals to ageclasses and cohorts by means of age determination
through otolith reading. The main effect of a substantial frequency of random errors in the age determinations would result in our present ‘cohorts’ actually
consisting of a mixture of fish from multiple, genetically distinct cohorts. Unrecognized mixing of this type
is expected to produce estimates of genetic differenti-
261
ation among cohorts that are biased downwards, and
thereby inflated estimates of Ne . Our present estimates
of effective size are so small, however, that it appears
unlikely that they are subject to significant upward
bias.
Another source of possible bias refers to the
genetic interpretation of zymograms at the sMDH3,4∗ isoloci where exhaustive inheritance studies are
lacking for the brown trout (cf. Taggart and Ferguson
1984). We have treated the ∗ 80 and ∗ 125 alleles as
belonging to different ‘dominant’ loci, but the segregation of both variant alleles at either or both loci cannot
be excluded on the basis of our present data. Our
genetic interpretation of the MDH zymograms is not
crucial for the present results, however. First, sMDH3,4∗ is only polymorphic at Locality II, and for this
population the exclusion of these loci only marginally affects the estimate of effective size. Further,
the results concerning, e.g., F-statistics (Table 2)
and statistical power (Figure 3) are based entirely on
co-dominant loci and do not include sMDH-3,4∗.
The temporal method for estimating effective size
is based on the assumption that observed allele
frequency shifts are due to genetic drift and sampling
error only, and immigration from genetically divergent populations might therefore bias the estimates of
Ne (Nei and Tajima 1981; Waples 1990; Jorde and
Ryman 1996). Although it appears unlikely that the
present populations are completely isolated, we do
not consider potential bias due to immigration as a
major problem when estimating effective size. The
large amount of differentiation between Locality I
and II suggests that the overall amount of gene flow
is quite restricted in this water system. Furthermore,
and as discussed above, the genotypic distributions
within each population appear compatible with those
expected in randomly mating populations without
substantial immigration.
Ignoring overlapping generations: Sampling from
populations with overlapping generations may result
in observed temporal allele frequency shifts that are
expected to deviate from those in populations with
discrete generations of the same effective size. Thus,
when estimating Ne from shifts over ‘short’ periods
of time, this deviation should be accounted for on the
basis of demographic information from the population
studied. Over longer time periods the need for such a
correction becomes progressively less important, but
it is unclear when the time span between samples is
large enough for this complication to be negligible. We
evaluated the consequences of ignoring the ‘overlapping generations effect’ in the present material through
comparing the observed amount of genetic change per
year to that expected from random genetic drift alone,
given our estimates of Ne and G (Tables 3 and 4).
When generations overlap the expected amount
of annual allele frequency change due to genetic
drift is determined by the annual effective population size (Na ), a quantity that relates to Ne as
Na ≈ Ne G, where G is the generation interval (Hill
1979). Thus, in order to assess the significance of
disturbing effects from overlapping generations, we
‘estimated’ Na in Locality II (which represents our
largest data set) directly from the observed annual
allele frequency shifts without accounting for the
sample age-structure. The estimates were based on
entire samples collected various numbers of years (1–
10) apart, all the age-classes within a sampling year
were pooled, and Na was calculated using the relation Na = t/(2Fk ), where t is the number of years
separating the samples. For comparison, Na was also
estimated from temporal allele frequency shifts generated in pseudo-random number computer simulations
in a population with overlapping generations and the
same effective size and demography (i.e., li and bi )
as estimated for Locality II. The simulations were
conducted as described by Jorde and Ryman (1995)
and Ryman (1997), and sampling from the simulated
population was performed 1–10 years apart maintaining the same age distribution as in the empirical
samples.
The empirical estimates of annual effective size
(Figure 4; panel A) show that this direct approach
results in considerable underestimation of Na for
samples collected only one or a few years apart.
This implies that the observed amount of temporal
genetic change in Locality II (corrected only for
sample size error) is larger than that expected from
genetic drift alone. The bias appears fairly small for
comparisons more than about one generation apart,
but we do not think that this tendency can be taken to
reflect a general phenomenon. The simulation results
(Figure 4; panel B), which are largely congruent with
the empirical observations, indicate that a downward
bias remains also for comparisons 10 years apart, i.e.,
almost two generations. They further indicate that
underestimation of Na is to be expected both when
the allele frequencies represent sample estimates and
when they are for the population as a whole. Thus, the
large allele frequency shifts observed in our data (that
exceed the expected amount of change due to genetic
262
Figure 4. Hypothetical point ‘estimates’ of annual effective size
(N̂a ) as they appear when the effects of overlapping generations
are ignored. A: Empirical estimates for Locality II. B: Simulated
estimates (based on 5000 replicate runs; × and are for samples
and the total population, respectively) for a population with the same
effective size, demographic characteristics, and sample age distribution as for Locality II. Each point estimate is based on average Fk
(Fk for the simulated total population) computed for all possible
pairwise combinations of allele frequencies a particular number of
years apart. “. . . The dotted lines (panel A) represent 95% confidence limits for the empirical Na estimates, whereas the stippled
straight lines (both panels) indicate the overall estimate of annual
effective size (N̂a ≈ N̂e Ĝ ≈ 48 × 6.2 ≈ 300). Note that the amount
of data behind each point estimate is larger for comparisons separated by a few years only; in panel A, for example, the underlying
number of Fk values are 156 and 40 for the estimates that are 1 and
10 years apart, respectively. See text for details.”
drift) mainly appear to reflect a true characteristic of
the population, rather than just ‘artifacts’ due to inadequate sampling design. Clearly, further theoretical
or simulation studies are required for a more general
evaluation of when the signal from random genetic
drift overrides the systematic short term changes and
sampling effects that are characteristic of populations
where generations overlap.
Implications for genetic monitoring: The ‘biodiversity
crisis’ has accentuated the demand for quick identification of populations that require special attention,
and temporal genetic data may be used to detect, for
example, genetic introgression, bottlenecks, or alarmingly small effective sizes (UNEP 1995; Luikart et
al. 1998; Laikre 1999). Some of the empirical observations of the present study are directly relevant to
such genetic monitoring and reinforce the results of
previous theoretical work. First, extensive sampling
over a series of years may be needed to detect significant temporal change or that the effective size of a
population is below some critical level of, say, Ne =
50 (e.g., Franklin 1980). Conversely, an observed
lack of statistically significant temporal heterogeneity
must be interpreted with great caution; such ‘temporal
stability’ does not necessarily imply a very large
effective size unless supported by a statistical power
analysis or independent ecological data.
Second, when dealing with populations where
generations overlap it is imperative to consider the
peculiarities of the allele frequency dynamics relative
to the discrete generation situation, for example
when estimating Ne . Likewise, considerable frequency
differences may be expected among cohorts, or
between samples dominated by one or a few cohorts,
also in populations of a fairly large effective size
(Ryman 1997). Thus, the observation of statistically
significant allele frequency differences should not
necessarily be considered an indication of introgression, the operation of selection, non-random sampling
of, e.g., family groups, or a remarkably small effective
population size.
Acknowledgements
We thank associate editor Robin Waples and two
anonymous reviewers for comments on an earlier
version of the manuscript. Gunnar Ståhl is acknowledged for valuable discussions and information
regarding the early phases of the ‘Lakes Bävervattnen’ project. The present study was supported
by grants to N.R. from the Swedish Natural Science
Research Council and from the Swedish research
program on Sustainable Coastal Zone Management,
SUCOZOMA, funded by the Foundation for Strategic
Environmental Research, MISTRA. L.L. acknowledges grants from The Swedish Research Council for
Environment, Agricultural Science and Spatial Planning (FORMAS) and from the Erik Philip-Sörensen
Foundation. P.E.J. was supported by the Research
Council of Norway.
263
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