Riolopical~~oumal
of thp Linnean S o c k 9 (1995), 54: 329-348. \Vith 7 figures
Limitations to the inference of gene flow at
regional geographic scales-an example
from the Pieris napi group (Lepidoptera:
Pieridae) in Europe
ADAM H. PORTER
Department ofBiologica1 Sciences, Bowling Green Uniuersio, Bowling Green, Ohio,
83403-021 2, U.S.A.
AND
HANSJURG GEIGER
zoo1ogische.r Institut der Universitat Bern, Baltzerstrasse 3, CH-3012 Bern, Switzerland
Recnved I .Seplember 199'3. accepkd fur puhhcatnun 20 September I904
\Ye used hicrarchical and paiwisc F-statistics to dcscribc genetic differentiation and infer gene
flow (hf)on local and re&mal scales within and among parapatric European butterfly taxa in
the Pierir napi (L.) p u p . \Vithin-population allozymc variability is consistently high, and local
rllertivc population sizes are inferred to be in the thousands of individuals. 'l'hc pairwisr analysis
yields an average neighbourliood area of radius 3.5 km. Among populations within most regions,
i' > 2 efrectivc individual!, population-' generation-'. Painvise romparisons
difterentiation is low and h
within the bn'tannica group show a dkjunction indicating that it is out of equilibrium, perhaps as
a result of secondary contact between highland and lowland groups. Comparison brtween rnen'dionalz.!
groups on mainland Italy and Corsica yields it"1> 12; this is surely too high and lack of equiljhrium
resulting from initial colonization is suspected. ' I h r hierarchical analysis indicates that 23 < hl < 88
among the taxa napi, byuniae and rneridiona1i.r that meet in hybrid zones; no effective genc flow
barrier exists among them. This high estimate could also result frotn rrccnt primary contact, but
such a genetic barrier should produce the 'edgc effects' seen in population genctir simulations,
and no evidence of this was found among geographically close samples of napi and hyoniar
populations from Switzerland. Studies of gene flow among geographic regions arc greatly limited
by the equilibrium assumption, though studirs of local diffcrentiation are much lcrs so. Population
studies of grnc Row on local scales at rekfiorial boundaries provide limitcd means of testing the
equilibiium assumption, and both regional and local analyses provide testable predictions about
local population structure. \Then the equilibrium assumption is not upheld, local pattcrns at
regional boundaries can procide historical information about primary vs. secondary rontact.
KEYWORDS :-/+tatistics
genetic population
enzyme electrophoresis.
isolation by distancc
ADDITIONAI,
systematics
~~
CONTENI'S
. . . . . . . . . .
Introduction
.
Geographic scale and genetic diffcrentiation .
'I'axonomy and natural history ofthe Pieninapigroup
. . . . . . .
Materials and methods .
. . . . . . . .
Electrophoresis
329
0024 4066/95/040329+20 $08.00/0
structure
specics-level
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0 1995 The Limean Society of London
330
A. H. PORI’EK AND H . GEIGER
Irrtrapopiilation variability . . . . . . .
Hierarchical F-statistics and grne flow
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Pairwise F-statistics and isolation by distancc . . .
Spatial autocorrelation of allele frequcncirs .
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Results
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Genetic variability within populations
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Hierarchical F-statistics .
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Pairwise F-statistics and isolation by distance .
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Spatial autocorrelation .
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Discussion .
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Violations involving seconciary contact .
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Violations involving rrccnt separation of populations .
Limitations of genetic data at regional scales: summary
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Additional aspects of Pierien‘rnupi group gerirtics
Acknowledgements .
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Rrfcrences .
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INTRODUCTION
Systematists defining species and subspecies boundaries make taxonomic
decisions based on their inferenccs about populational processes, particularly
gene flow and adaptation (Mayr, 1963). These inferences are derived from
patterns of variation within and among populations, and among regional groups
of populations. A regional geographic scale is considered here to be at least
two orders of magnitude larger than individuals move during their lifetimes.
The inferences of systematists arc typically made intuitively, without reference
to quantitative or statistical models explicitly linking patterns to underlying
processes. However, the same populational processes have been studied in much
greater detail at local geographic scales by population biologists, and appropriate
models are now available to extend quantitative, statistically based inferences
to regional geographic scales.
In this paper, we review the basic principles of these models and how they
can be applied to the study of the processes responsible for regional differentiation.
We then turn to an analysis of regional geographic differentiation of pierid
butterflies in the Pieris nopi (L.) complex to illustrate some of the inferences
that can be made in practice, and where further data are needed before
underlying processes can be adequately understood. In our analysis, we will be
particularly interested to infer the status of genetic isolation, or its complement,
gene flow, across the boundaries of regionally defined units, because the ability
to test such inferences is of great value to population biologists, conservation
biologists and systematists.
Geogruphic scale and genetic dgerentiution
The geographic scale at which patterns of population differentiation are
studied influence the interpretation of processes responsible for that differentiation.
Gene flow, genetic drift, natural selection and mutation eventually result in an
equilibrium level of genetic differentiation (Wright, 1931). If differentiation
among populations is described by Nei’s (1973) GsT, then the time in generations
to approach half the distance to an equilibrium level of differentiation was
found by Crow & Aoki (1984) to be t z (In 2)/[(4M+l)/n], where n is the
effective population size and A4 is the effective number of individuals exchanged
per population per generation. For the purposes of empirical studies, the time
REGIONAL GENE FLOW
71 1
needed to approach equilibrium from a major deviation (perhaps from range
expansion or fragmentation) is on the order of about t z 3n generations; much
less if the initial deviation is small or M is high. At local geographic scales,
where populations are often relatively small (n < lOOO), genetic drift can
operate at a relatively ‘fast’ rate to promote differentiation. In populations of
this size, selection at a locus must be relatively strong to overcome gene flow
and drift, and even then, gene flow and drift will still contribute to differentiation.
For selection to have an important influence on average levels of differentiation
among populations, it must be strong enough to overcome drift and gene flow
at numerous loci simultaneously. At local scales, gene flow and drift are
probably the most important factors influencing average differentiation for most
loci, and selection will be important for relatively few loci.
As the geographic area of study is expanded from a local to a regional
scale, a change occurs in the relative importance of processes controlling genetic
differentiation. Effective population sizes of regions are larger because local
populations are accumulated, so genetic drift of entire population groups is far
slower (Kimura, 1983) and it will take much longer for initial deviations from
equilibrium to be reduced. Geographic distances are also greater and perimeterto-area effects are more likely to come into play: only populations near the
boundaries between groups are likely to contribute to gene flow among groups
and the proportion of individuals moving among groups will be lower. Natural
selection also has greater opportunity to influence thc pattern of regional
differentiation because it will encounter less resistance from drift or from
homogenization by gene flow from outside the region-more profound regional
differentiation can be produced in traits experiencing lower selection coefficients.
Traits under selection regionally are thus likely to eventually become nearly
fixed even if there is reasonably strong gene flow at local scales across regional
boundaries. Even functionally independent traits may come to have common
boundaries caused by selection and genetic interactions among loci (Barton,
1983); nearby clines in independent traits converge and hybrid zones become
established at the boundaries (Barton & Hewitt, 1985). Polygenic traits under
selection are likely to maintain their genetic and phenotypic ‘cohesion’ regionally,
and traits under different selection regimes regionally will maintain their
geographic boundaries indefinitely. Even so, traits with very weak selection
coefficients will still have patterns of regional geographic differentiation controlled
largely by gene flow and drift. Neutral traits and those beneficial in all regions
are free to cross the boundaries among regions, being delayed but not stopped
at the boundary (Barton & Bengsston, 1986). This provides a limitation on the
ability of systematists to make inferences about underlying processes from
regionally distinct ‘diagnostic’ traits: at regional geographic scales, boundaries
in such traits may not be evidence of more profound genetic isolation, but
may instead be limited to those genes involved in the trait.
Porter (1990) suggested the use of statistics that describe genetic differentiation
hierarchically (Wright, 1978; Weir & Cockerham, 1984) to make inferences
about gene flow among population groups at a regional scale, because these
descriptive statistics are linked to gene flow in well-established models of the
evolutionary process (Wright, 1931, 1969, 1978; Slatkin & Barton, 1989). These
statistics can be used in a limited way to test taxonomic hypotheses based on
morpholo<gy.The inferences about gene flow rates require several assumptions,
-
332
A. H. PORTER AND H. GEIGER
discussed by Porter (1990). The most important of these include that populations
and regions are ncar equilibrium levels of differentiation, population sizes and
population group sizes are approximately equal, and loci are approximately
neutral at populational and regional scales.
We take a sequential approach to the problem in the absence of knowledge
of the status of the equilibrium assumption. First, we apply hierarchical Fstatistics (Porter, 1990) and pairwise F-statistics (Slatkin, 1993), both of which
assume global equilibrium, to produce estimates of gene flow among geographic
regions in the Pieris nap; group in Europe. We also apply a spatial autocorrelation
analysis (Sokal & Oden, 1978a,b) to examine its utility relative to F-statistics.
Our ‘conclusions’ reflect the equilibrium assumption, and we then discuss the
limitations on these conclusions. We end with testable predictions about rates
of gene flow at local population scales and at regional boundaries. The next
step is to compare these predictions to local gene flow rates in hybrid zones
at the boundaries between regions; this work is in progress. Ultimately, results
of such comparisons can either provide support for the use of the equilibrium
assumption, or else provide historical information about primary or secondary
contact.
Taxonomy and natural histoy
of the
Pieris napi group
The Pieris nap; group has a holarctic distribution and is differentiated into
numerous geographical forms (Geiger & Shapiro, 1992), many with taxonomic
names assigned. Some taxa are clearly separate species and have sympatric
populations (Hovanitz, 1963) showing fixed allozyme differences indicative of
genetic isolation (Geiger & Scholl, 1985). Others with parapatric or allopatric
distributions show less allozyme differentiation (Geiger & Scholl, 1985; Geiger
& Shapiro, 1992) and their taxonomic status remains unresolved.
Here we address differentiation among five European taxa of the nap; group:
nap;, meridionalis, byoniae, adalwinda, and britannica; their approximate distributions
are shown in Figure 1. There are no consistent genitalic differences among
these taxa (Lorkovic, 1962), but they differ in several life-history and wing
pattern traits. Life-history differences are mainly involved in the control of
pupal diapause, which influences the number of annual generations. These
show strong adaptation to local conditions and do not agree exactly with
taxonomic boundaries. There are also differences in wing patterns. The European
taxa form hybrid zones wherever their ranges contact (Petersen, 1955, 1963;
Lorkovic, 1962), and crosses between individuals from widely separated localities
are sometimes barren in the laboratory (Lorkovic, 1962; Bowden, 1972).
Throughout, we use Latin binomials for convenience and without intending
implications about taxonomic status.
MATERIAIS AND METHODS
The study populations and their current taxonomic status are given in Table
1, and shown in relation to regional and taxonomic boundaries in Figures 1
and 2.
REGIONAI. GENE FLOW
333
Electrophoresis
Individuals were sampled haphazardly from natural populations, transported
alive or on dry ice to Bern and stored at -70°C until electrophoresis. Sample
sizes are given in Table 1. Wings and genitalia were saved as vouchers and
have been retained by HJG.
The head and thorax of each specimen were homogenized in 4 volumes of
buffer (0.05 M Tris-HC1, pH = 8.0). We used starch gel electrophoresis following
slightly modified standardized procedures (Ayah et al., 1972; Geiger, 198 I).
Twenty-one enzyme loci were scored: adenylate kinase (2 loci: AK-1, AK-2;
enzyme commission number 2.7.4.7), aldolase (ALDO; 4.1.2.13), arginine kinase
(APK;), fumarase (FUM; 4.2.1.2), glutamic-oxaloacetic transaminase (GOT-1,
GOT-2; 2.6.1. I), glutamic-pyruvic transaminase (GPT; 2.6.1.2), glyceraldehyde-3phosphate dehydrogenase (GAPDH; 1.2.1.12), a-glycerophosphate dehydrogenase
334
A. H. PORTER AND H. GEIGER
TABLE
1. Study populations a n d thcir taxonomic classification
Number
~
Name
~~~~
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
n
Grachwil, nr. Bern, Switzerland
Rremgartenwald, Bern, Swit~erland
Steffisburg, Switzerland
Uetendorf, Switzerland
Belp, SwitLerland
1.r Cnty, nr. Neuchgtel, Switzerland
lklenbach, Switzerland
Zweilutschinen, Switzerland
Halap, Hungary
Debrccen, Hungary
h e , France
Le Grau du Roi, France
Forit Romeu, 1:rance
Colomhicr, France
Pforzheim, Germany
L a k e n , Denmark
Saas Almagell, Switzerland
Grosse Scheidegg, Switzerland
Morteratsch, Switzerland
Albula Pass, north side, Switzerland
Halsrn Lake, nr. Binn, Switzerland
Kandcrsteg, Switzerland
Bois de Begnisch, Canton Jura, Switzerland
Blatten, Switzerland
Nova Gorika, Croatia
Modena, Italy
Scrramazzoni, Italy
Silla, Italy
Lignano, Italy
Cortc, Corsica, France
Barchetta, Corsica, France
Aberdeen, Scotland
Kelvinhead, Kilsyth, Scotland
Wester Hardmuir Forest, nr. Nairn, Scotland
South Cave, North Humbcrsidr, UK
Oban, Scotland
ShcriKmuir, Dunhlanr, Scotland
IL(ystcse, Norway
Abisko, Sweden
Date
Taxon
~ ~ ~ ~ _ _ _ _
~
39
11
12
13
12
12
9
15
23
24
18
22
16
15
9
12
24
31
11
10
11
29
20
12
12
I1
10
II
20
14
8
16
30
24
12
20
21
16
6
late Apr/mid May 1980 napi
9 May 1978
nap2
nap;
14 May 1979
napz
14 May 1979
napz
25 hfay I979
16 July 1979
nap;
9 September 1982
napi
30 May 1979
napi
napi
12 April 1983
napi
12 April 1983
19 October 1981
napi
30 June 1980
napi
3 June I979
napi
napi
2 ,June 1979
27 hlay 1979
napi
1 August 1984
napi
hryoniae
14 July 1982
bryoniae
3 August 1981
15 July 1982
bryoniae
16 July 1982
hryoniae
hryoniae
31 July 1980
7 July 1982
bryoniae
hryoniae
20 June 1983
8 July 1982
bryoniae
meridzona1i.r
30 May 1982
23 31 May 1980
meridionalis
21 August 1980
meridzonalzs
27 August 1978
meridiona1i.c
meridionalic
24 August 1978
27 hlay 1983
meridionalir
29 May 1983
meridionali~
28 August 1983
britannica
28 May 1982
hntannzca
28 hlay 1982
britannica
2 August 1982
hritannica
20 August 1983
hntannica
3 August 1983
hritannira
26 July 1984
adalwinda
adalwinda
23-31 July 1982
(ctGPDH; 1.1.1.8), hexokinase (HK; 2.7.1.l), isocitrate dehydrogenase (IDH-1,
IDH-2; 1.1.1.42), malate dehydrogenase (MDH-1, MDH-2; 1.1.1.37), malic
1.1.1.40), phosphoglucomutase
(PGM; 2.7.5. l),
6enzyme
(ME- 1;
phosphogluconate dehydrogenase (GPGH; 1.1.1.43), phosphoglucose isomerase
(PGI; 5.3.1.9), pyruvate kinase (PK; 2.7.1.40), and superoxide dismutase (SOD1; 1.15.1.1). Banding patterns were scored in comparison to mobilities of a
Pieris brussicae standard. Several loci are typically monomorphic in the nupi
group and related species (Geiger & Scholl, 1985; Geiger & Shapiro, 1992).
These loci were not scored in eight populations, and sampled in only a few
representative individuals in other populations. All individuals were scored for
nine loci known to be polymorphic from earlier study (GOT-1, GOT-2, IDH1, IDH-2, MDH-1, MDH-2, GPGD, PGI, PGM; Geiger 1981), and these nine
loci were used in studies of local and regional differentiation.
REGIONAL GENE
mw
335
Figure 2. Collrction localities in Switzerland, with t h ~approximate range of byuniae in regions
above 1200 m (stippled). Circles: nupi; squares: hyonzae. Population key in Tablc 2.
Intrapopulution variabilig
Loci within populations were assayed for deviations from Hardy-Weinberg
genotypic frequencies using log-likelihood contingency table analyses (Sokal &
Rohlf, 198 1). Genetic variability was estimated for the 3 1 populations where
21 loci were sampled, using the following four methods. We considered a locus
to be polymorphic if more than one allele was detected in our sample, and
calculated the percent of polymorphic loci ('lop) from this criterion. We counted
the heterozygous individuals at each locus and determined the average proportion
of individuals heterozygous at each locus (Hob?).From allele frequencies, we
calculated the average proportion of individuals expected to be heterozygous at
each locus assuming Hardy-Weinberg proportions (HJ. Finally, we calculated
the mean number of alleles per locus sampled (A). All these values are likely
to be slight underestimates because not all individuals were sampled at all loci,
and because alleles with very similar electrophoretic mobilities may be
inadvertently pooled.
Using A, it is possible to determine an approximate effective population size
(n), if the mutation rate (p) is known, by solving the equation
for n (Ewens, 1964: eqn. 5). Solutions were obtained numerically for different
values of 4 and p using a Mathematicum notebook (Wolfram, 1991), available on
request from AHP. These were calculated only for the 31 populations wherein
all 21 loci were scored. Our interpretation of these n estimates is qualitative
due to the assumptions involved.
336
A H PORTb,R AND H GEIGbR
Hzerurchzcal F-statzstzcs and gene JOW
Details of the theory relating gene flow and population differcntiation are
extensive and we will only highlight them here. The original F-statistics (Wright,
1931) were derived as population parameters, rather than sample statistics, to
describe genetic differentiation among individuals within populations, among
individuals within the total group of populations, and among populations in
the group; deviations caused by sampling errors were not addressed. Cockerham
(1969, 1973) showed that Wright's F-statistics could be derived as parameters
in a nested analysis of variance, allowing biases from sampling to be taken
into account. Weir & Cockerham (1984) extended the estimation procedure to
multiple alleles and loci and to the next hierarchical level, differentiation among
groups of populations, and within groups when there are more than one group.
Slatkin (1985b, 1987), elaborating on a relationship discovered by Wright
(1931), lead the development of the analysis of gene flow M from F-statistics.
Slatkin & Barton (1989) showed that for most data sets, the approach using
F-statistics was superior to that of rare alleles (Slatkin, 1985a), though they
are both derived from the samc underlying population model. Cockerham &
Weir (1987, 1993) developed the statistical theory of estimation of A4 from Fstatistics, extending it to higher hierarchical levels. Crow & Aoki (1984) extended
these ideas from Wright's (1931) island model to a more realistic stepping-stone
model, and Slatkin & Barton (1989) derived the general relationship between
this and the continuous, isolation-by-distance model. When the isolation-bydistance model is conceived as a series of adjacent genetic neighbourhoods, it
converges to a stepping-stone model. The outcome is that near equilibrium,
the relationship between gene flow and genetic differentiation is very similar in
stepping-stone and island models as long as the number of local populations is
large (Crow & Aoki, 1984).
The notation for F-statistics is diverse and unstable, particularly with regard
to statistical estimators and population parameters. We use the following notation
and formulae for hierarchical F-statistics. Following Wright (193 l), the subscript
S means (sub)population and subscript T is the total population, made by
pooling all populations. Following Porter (1990), the subscript G represents
an intermediate level of population groups, made up of pooled populations,
and here accounts for regional differentiation. The estimated values have hats
(A) whereas the population parameters do not, and bars (-) indicate values
taken as weighted averages over alleles and loci as recommended by Weir &
Cockerham (1984). F57 describes average differentiation among populations,
ignoring any regional effects. Its statistical estimator is FyT and is equivalent to
8 of Weir & Cockcrham (1984) and 8, of Cockerham & Weir (1987).
describes average diff+entiation among regions. Its statistical estimator is p(,7;
this is equivalent to OL of Weir & Cockerham (1984) and 8, of Cockerham &
Weir (1987). F5(7
describes differentiation within regions. Its statistical estimator
is psc,,equivalent to 8, and p of Weir & Cockerham (1984) and Cockerham
& Weir (1987), respectively.
Gene flow A4 was derived from the approximate relationship
p(,,
(Wright, 1931; Cockerhain & Weir, 1987), estimated statistically
h
' as
REGIONAI. GENE FL0\2’
337
(Cockerham & Weir, 1987) where xx indicates subscripts ST, GC or SG. M is
the average effective number of individuals exchanged per generation between
populations (for S T or SG) or regions (for G T ) . Values of Mix> 0.5 are strong
enough to swamp appreciable differentiation caused by genetic drift (Wright,
1931), and A&,T > 0.5 has been considered high enough that gene flow is likely
on a regional scale, as when taxonomic hypotheses about genetic isolation are
becomes high, accuracy is likely to be
being tested (Porter, 1990). As
diminished (but strong qualitative conclusions obviously apply) due to assumptions
were calculated by the
made in the derivation. Standard deviations for Fyy
jackknife method recommended by Weir & Cockerham (1984), dropping
individual loci. From these, 95% confidence intervals were obtained using
& 1.96 (SD), and error estimates on &Ix,
were obtained from these limits using
approximation (2) (Porter, 1990). Note that even though 0 < Fxx< 1, values of
F,x < 0 are sometimes produced during the course of statistical estimation when
populations are very similar. When converted to kxx,
these were scored as
panmictic. A computer program for these calculations is available from AHP
on request.
We looked for structure among all remaining taxa in Europe, and also in
more localized areas, especially between island and mainland taxa, and among
central European taxa. Members of the nap; group differ in annual number of
generations and this may in turn affect gene flow rates, so F,, was also
calculated for taxa and geographic regions separately.
ax,
Pairwise F-statistics and isolation by distance
A genetic distance measure developed by Reynolds et al. (1983) is essentially
Fy7.calculated
between pairs of populations, incorporating the appropriate
statistical sampling theory. Slatkin (1993) developed theory and simulations
relating these painvise F-statistics to gene flow M in stepping-stone and isolationby-distance models. The underlying concept is that as populations are separated
by greater distances, genes are less likely to traverse the distance in one
generation but may do so after several generations of smaller movements.
Populations at greater distances are more likely to accumulate differences by
drift and mutation, and the resulting differentiation will be reflected by the
painvise Fy7 values.
using approximation
Slatkin’s (1993) approach was to convert pairwise Frr to
(Z), then to plot these against geographic distance. He found the log-log plot
to be approximately linear, with a negative slope indicative of isolation by
distance and the y-intercept an approximation of the local effective population
size. Our data had numerous values with painvise F s T < 0, yielding undefined
values of &
soI
,
that significant biases would be inpoduced by omitting these
from the analysis. Instead, we fit the pairwise Fyr values to the function
y = 1/(4x+1); a rearrangement of approximation (2), where the x-axis is the
great-circle distance between pairs of populations. The x-intercept of this function
then estimates the radius of the average local genetic neighbourhood area.
338
A. H. PORI'KR AND H. GEIGER
If particular sets of populations are genetically isolated or out of equilibrium
relative to the remainder, then these will often show up graphically as
discontinuities in the painvise analysis (Slatkin, 1993). This removes a restriction
of the hierarchical approach, namely that the original groupings are imposed
at the b e p n i n g of the analysis. In the Pieris nupi group, the taxonomic
groupings are based mainly on small differences in wing pattern and are
controversial among systematists, and relaxing this assumption effectively tests
the utility of the original groupings. As usual with plots of genetic vs. geographic
distance, the points are not independent and no statistical tests of slope and
intercept values, short of bootstrap methods, are available. With large data sets,
even the calculation of pairwise Fs7 is computationally intensive and bootstrap
tests were not feasible.
Spatial autocorrelation o f allele j-equencies
Another approach to the analysis of geographic differentiation is through
spatial autocorrelation (Sokal & Oden, 1978a,b). Spatial autocorrelation decribes
the extent to which alleles are correlated in populations separated by successively
greater spatial distances. With isolation by distance, allele frequencies should be
increasingly correlated at closer distances (stimulated by Sokal & Oden [1978b],
although we are unaware of any study of the analytical relationship of
autocorrelation statistics to population processes). However, when nearby
populations are separated by a barrier to gene exchange, their frequencies
should be uncorrelated. In this analysis, we classified population pairs as to
whether they were of the same or different taxa, then used Moran's I to
calculate distance-corrected correlograms (Sokal & Oden, 1978a,b) for withintaxon and between-taxon autocorrelations separately; these were compared
qualitatively. Our distance classes were the intervals between 0, 25, 50, 100,
250, 500, 1000, 2500 and 5000 km, with corresponding sample size of 15, 26,
34, 52, 106, 157, 309 and 42 population pairs. We calculated significance at
a = 0.05 for each allele independently, following Sokal & Oden (1978a). We
are not familiar with any method for combining autocorrelations of different
alleles and loci into a single statistical test, but a Bonferroni correction (Rice,
1989) was used to find globally significant autocorrelations.
RESULIS
Genetic variabilio within populations
Our data set is available from the Librarian of the Linnean Society of
London, Burlington House, Piccadilly, London W 1V OLQ. There were occasional
significant deviations from Hardy-Weinberg genotypic proportions, but there
were no apparent patterns within populations or loci; when a Bonferroni
correction was applied (Rice, 1989), the significance disappeared.
All populations maintain high genetic variability (Table 2). This high genetic
variability in turn is likely to reflect large effective population sizes. Estimates
calculated from A using equation ( I ) were calculated for a range of possible
values of the mutation rate p. Even assuming a maximal level of p =
there are still effectively at least several hundred individuals per population
REGIONAL GENE H,OW
339
T A B I2.. ~Genetic variability scores (s.c.) for all populations, based on 21 loci. A: mean number
of alleles per locus; %P: the percent of loci polymorphic in the population (the values were the
samc regardless of the critcrion used to determine polymorphism); H,,,,,: the estimated proportion
of individuals observcd to be heterozygous, averaged over loci; H,,,: the cstimated proportion of
individuals cxpected to he heterozygous, based on Hardy-Weinbcrg proportions. Standard errors
from jackknifes over loci
Number
~~~~
1
4
5
7
8
9
I0
11
12
13
17
18
I9
20
21
22
23
24
25
26
27
29
30
31
32
33
34
35
37
39
A
Population
~~
Grichwil
Urtendorf
Belp
Erlenbach
Zweilutschiricn
Halap
Debreccn
Elne
1,c Grau du Roi
1:ont Romeu
Saas AlmagcII
G r o w Scheidegg
Morteratsrh
Albula Pass
Halsen Lake
Kanderstcg
Bois de Begnisrh
Blatten
Nova Gorika
Moderia
Serramazzoni
Iignano
Corte
Barchctta
Aberdeen
Kelvinhead
\Yester Hardmuir 1:orcst
South Cave
Sheriffmuir
Abisko
O/OP
-~
~~
2.25
1.55
1.55
1.60
1.40
1.9.5
1.85
1.60
1.70
l..55
1.50
1.60
1.55
1.40
1.60
1.55
1.55
1.3.5
1.80
1.50
1.50
1.70
1.80
1.45
2.00
1.55
I .45
1.55
1.70
1.65
(0.02)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
(0.01)
45.0
35.0
35.0
40.0
30.0
50.0
50.0
45.0
35.0
3.5.0
35.0
40.0
35.0
30.0
35.0
40.0
35.0
20.0
40.0
35.0
35.0
40.0
35.0
30.0
50.0
30.0
25.0
35.0
45.0
35.0
(0.6)
(0.5)
(0.5)
(0.5)
(0.5)
(0.6)
(0.6)
(0.6)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.4)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.6)
(0.5)
(0.5)
(0.5)
(0.6)
(0.5)
fi,,,,,
-~
0.147
0.128
0.101
0.150
0.097
0. I14
0. I20
0.159
0.099
0.089
0.072
0.104
0.090
0.1 16
0.107
0.100
0.104
0.080
0.1 17
0.074
0.123
0. I I6
0.160
0.083
0.153
0.1 I7
0.13 1
0.157
0. I94
0. I89
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0,001)
(0.002)
(0.002)
(0.002)
(0.002)
(0.00 1)
(0.002)
(0.002)
(0.002)
(0.001)
(0.002)
(0.002)
(0.003)
(0.002)
(0.002)
(0.003)
(0.003)
(0.003)
(0.003)
(0.003)
0.108
0.100
0.072
0.095
0.064
0.093
0.099
0.102
0.080
0.061
0,055
0.077
0.080
0.082
0.081
0.068
0.07.5
0.076
0.075
0.072
0.078
0.083
0.1 1 I
0.06.5
0.123
0.075
0.074
0.10 I
0. I05
0.130
(0.002)
(0.002)
(0.001)
(0.002)
(0.002)
(0.001)
(0.00 I )
(0.002)
(0.002)
(0.001)
(0.001j
(0.001)
(0.001j
(0.002)
(0.001)
(0.001)
(0,001)
(0.002)
(0.001)
(0.001)
(0.001)
(0.002)
(0.002)
(0.001)
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0,002)
throughout the nap; group. With levels of p between lo-' and lo-'' as in most
animal species, there are probably effectively several thousand individuals in
most populations.
Hierarchical F-statistic5
Genetic differentiation among populations within taxonomic groups (Table 3)
is very low, except among the adalwinda and britannica populations. This
corresponds to gene flow levels which are all significantly greater than M y I = 0.5,
and indicates significant homogenizing gene flow is likely to be occurring at
broad geographic scales. In the brztannica populations, the locus responsible for
most differentiation was MDH-I, which had a high frequency of allele A at
Aberdeen (a trait shared with napi), but more of allele B in the remaining
populations. In adalwinda, there were only two populations with limited numbers
so overinterpretation is possible, but Abisko had high frequencies of MDH- 1
alleles J and K relative to most other napi-group populations.
Genetic differentiation among regions is also very low (Table 4), and the
A. H. PORI'ER AND H. GEIGER
340
TABLE3.
k5Tand corresponding gene flow estimates (US7)within
taxonomically and geographically defined groups
Taxon
nu@
bryonzae
mendzonalzs
Corsica only
without Corsica
bntannzcu
adalwznda
f757
(SE)
Lower
bound
0.0226
0.0277
0.0052
0.0079
0.0003
0.1322
0.1010
0.0006
0.0009
0.0017
0.0029
0.0020
0.0145
00110
9.4
7.3
16
9.8
21
0.90
1.3
Upper
bound
My,
11
8.8
48
32
980
1.6
2.2
13
11
panmictic
panmictic
panmictic
5.1
6.6
corresponding &I values high. Taking F57 at the broadest scale among all
populations, the lower confidence limit at &Isir = 1.6 is well above &Isr= 0.5,
suggesting widespread gene flow across the entire continent. When this is
broken into differentiation among regions, the lower confidence limit to FLT
gives a high M(,r = 2.3, suggesting that gene flow across regional and taxonomic
boundaries is promoting significant homogenization.
At the smaller geographic scale between napi, blyoniae and meridionalzs, F57 is
considerably lower and the corresponding
higher than at the larger scale.
Among groups, pc,7 remains small and the lower confidence limit to intergroup
gene flow is &IGT = 23. However, between britannica and nap;, which here also
reflects differentiation between Britain and Europe because of the sampling
pattern, gene flow appears much more limited. Even though FyT remains low
enough that average gene flow seems high at A& = 2.1, the mean withinTABM4. Estimates of genetic differentiation and corresponding gene
flow across taxonomic and geographic boundaries
Taxa
~
~
(SE)
&S
~
~
~~
~~
Lower
bound
Upper
bound
~
nap!, bryoniue, meridionalis, britannica, udalminda
?GI
0.0598
0.0063
2.3
FSI
0.0887
0.0076
1.6
F,.
0.1025
0.0090
I .4
nap!, byoniae, meridinnalis
FC. r
0.0069
0.0007
23
F\ I
0.0258
0.0008
7.9
J%,
0.0284
0.00 I0
7.0
nap!, britannica
F,,
I
0.1100
0.0129
1.1
FS7
0.1066
0.0105
1.2
F,.
0.1597
0.0165
0.72
Cofsica, mainland meridionalis
Fc;I
0.0089
0.002 1
12
?Tr
0.0052
0.0017
16
FSG
0.0101
0.0030
9.1
3.9
2.6
2.2
36
9.5
8.5
2.0
2.1
1.3
28
48
25
11
5.5
4.8
88
12
I1
7.1
5.3
3.8
panmictic
panrnictic
panmictic
REGIONAL GENE FLOW
34 1
group value of Msc;= 1.3 shows that gene flow is likely to be restricted within,
rather than between, these regions. This was unexpected because the English
Channel seems a likely barrier to gene flow, but differentiation between Corsica
and Italian meridionalis shows a similar pattern. There, the highest level of
differentiation from 95% confidencc limits still yields a remarkably high gene
flow rate of M(,7 = 12, suggesting that the barrier posed by the Mediterranean
may not be particularly effective. However, more likely in both these island
cases are difficulties with the equilibrium assumption, discussed below.
Paimise F-statistics and isolation by distance
Painvise py7for all population pairs are shown in Fig. 3, and inspection
reveals three separate clouds of points. The points in the upper central region
prove to be associated with the britannica populations (Fig. 4), and indicate that
this population grouping, as defined taxonomically, is not in equilibrium with
.
.. .
*
..:
...
.*
.
.. ".'
t
.
.
8
'
'
'
*
.
.
*.
a * .
~
0
1500
2000
Geographic distance (km)
500
1000
Figure 3 Pairwise j 5 rvalue5 vs great-circle distance (x) for
0.4
dII
2500
3000
pairs of populations
. .
[
0
.
... .
'r '
..,..
**:
..
.
0
500
1000
1500
2000
2500
3000
Geographic distance (km)
Figure 4. Subset of pairwise E,, values in Fig. 3 resulting from comparisons involving bntannira
populations. The discontinuity indicates a genetic disjunction within this regional <grouping.
A. H. PORTER AND H. GEIGER
342
.
h
IE4"
I .
I . . . . .
0
500
.
1000
1500
2000
Geographic distance (km)
2500
3000
Figurc 5. Pairwise I,, valucs vs. great-circle distance ( x ) excluding hritannica populations. Thc line
is the Icast-squares regression 0 1 Fs, vs. 1 /(4x+ I ) , appropriate lor tlrc is(,lation-hy-distancc model,
and drops sharply t>clow x = 20 km.
respect to its Fs7 values. Figure 5 shows the remaining data with a best-fit
curve appropriate for the isolation-by-distance model at FYT= 0.03 - 0.45/(4x+ 1).
The interccpt 2 = 3.5 km represents the estimated radius of the average local
neighbourhood area. The cloud at the far right of Fig. 3 is associated with
the adalwinda populations. Its placement above the best-fit line suggcsts that
these populations may also be out of equilibrium with the remainder of the
populations in central Europe, but the small adalwinda samples make this
interpretation tentative and they were not removed from the analysis.
Spatial autocorrelation
Figure 6 shows corrclograms for four loci of the nine polymorphic loci,
partitioned into autocorrelations of populations within the same regional
taxonomic grouping and autocorrelations of populations in different groupings.
The other loci showed comparable results, as did autocorrelations using the
entire data set without regard to regional boundaries. Considerable variation is
apparent, consistent with the painvise analysis above, and none were significantly
different from zero after a Bonferroni correction was applied. Comparison of
within- vs. between-region autocorrelations givcs no hint of a pattern consistent
with increased genetic isolation at the taxonomic boundaries.
IIISCUSSION
The estimation of gene flow rates from genetic data requires that gene flow,
genetic drift and mutation have approached their equilibrium, and there appear
to be two types of violations of this assumption in different subsets of our data.
We will discuss these violations in detail before addressing the more challenging
question of the general utility of the genetic data. We propose that analyses of
genetic differentiation at regional geographic scales play an important role in
REGIONAL GENE FLOiY
Within taxon
't
343
Across taxon boundaries
Zdh-1
Idh-l
lt
0.5
0.5
0
0
-0.5
-0.5
-1
-1
Idh-2
1
0.5
0.5
0
0
-0.5
1dh-2
1
-0.5
-1
-1
1
Pgi
1
0.5
0.5
0
0
Pgi
-0.5
-0.5
6
4
0
(3
QQ
t
@
4
0
'0
d
' o 0."
@ + + %
Distance class
Distance class
figure 6. Distance-corrected corrclograms representing spatial autocorrelations (Mordn's I ) for all
alleles at four loci. Left column: comparisons involving population pairs of the same taxon (region);
right rolumn: population pairs from different taxa (rrgions); circles: P < 0.05. Significance was
assessed separately for each allele.
our understanding of the causes of genetic structure, but because of their
limitations they must be supported by studies on local scales.
Violations involving seconday contact
The disjunct painvise F-statistics within P. britannica (Fig. 4) shows this
population group to be out of equilibrium with respect to gene flow and drift.
344
A. H. PORI'ER AND H. GEIGER
Regarding gene flow rates, there may be two explanations, representing extremes
of a continuum. At one extreme is that gene flow is strong, but secondary
contact has occurred in northern Britain between a northern population group,
perhaps endemic since glacial times, and populations from a more recent range
expansion of P. napi from continental Europe. At the other extreme is genetic
isolation among some sets of populations presently grouped within P. britannica.
The truth may lie somewhere in the middle and a hybrid zone, with partial
restriction on the rate of introgression (Barton & Hewitt, 1983), should be
sought between the higher-elevation, univoltine group of populations (Lees,
1970) and the remaining, multivoltine populations. A similar association between
a hybrid zone and life history differences occurs between P. napi and P. byoniae
in the Alps (Petersen, 1963).
Fortunately, there are simple solutions to this type of violation of the
equilibrium assumption. In our large data set wherein the P. britannica group
is a small part, we simply dropped it from further analyses. Alternatively,
Slatkin (1993) divided his data into subsets that did not appear to violate the
equilibrium assumption, verified their geographic continuity, then analysed
genetic differentiation in them separately. But one must be careful in doing so
when operating on a regional scale, because the second type of violation is
cryptic.
Violations involving recent separation
of populationr
The comparison between P. meridionalis on Corsica and the Italian peninsula
yielded a high estimate of gene flow (Mc,T 12, gen-', using the lower ci;
Table 4) across this significant water barrier. This value seems to be fantasy,
even though gene flow appears to be very high (at M t r > 21 gen-') within
mainland P. meridionalzs (Table 3). If vagility were indeed high enough in P.
meridionalis that this saltwater barrier were regularly crossed, we would also
expect to see occasional 'pure' P. meridionalis phenotypes appearing along the
south coast of Francc or north of the Alps, but none are found. Reports of
butterflies being carried by storms typically involve taxa exhibiting large
migrations (e.g., Larsen & Pedgley, 1983)pmost butterflies do not fly in storms,
and fly near the boundary layer during windy conditions-and in any case 12
gen-' is a large number to attribute to accidental dispersal (meridionah has up
to five gens yr-I).
We are left with the impression that the Corsican population group is out
of equilibrium with the mainland population, with high similarity (p(,r,indicating
not gene flow, but rather that not enough time has elapsed for mutation
accumulation and genetic drift to reach equilibrium levels of divergence between
these groups. Estimates of local population sizes on Corsica from the number
of alleles in populations are on the order of f l e % 500 (see below), and it is
not unreasonable to expect that Corsica as a whole has an effective population
size of IO5-l0". Using t % 1n(2)/[(4M+l)/n] (Crow & Aolu, 1984), this implies
that even complete genetic isolation from the mainland as long as t % 10' years
ago would still yield a substantial, spurious 'gene flow' estimate.
The lack of equilibrium involving Corsica highlights the limitations for
interpreting
among the remaining groups. It is well documented that the
REGIONAL GENE FLOIV
345
remaining groups meet in hybrid zones (Petersen, 1963), and that survivorship
in 6, broods is high (barring inbreeding depression; Lorkovic, 1962; Bowden,
1972). It is thus reasonable to presuppose that M , even if partially limited by
the hybrid zones (Barton & Hewitt, 1985), would be substantial across regional
boundaries, especially given the long, geographically continuous contact areas.
It is satisfying that MGT among napi, b?yoniae and meridionalis agrees with this
expectation. Unfortunately, regional population sizes for these taxa are likely to
be much higher than for Corsica. Thus, even if genetic isolation had evolved
among napi, b?yoniae and meridionalis within the last 10' or perhaps more
generations, we could still obtain such 'gene flow' estimates spuriously from the
hierarchical analysis.
However, if a parapatric species boundary has indeed arisen within the last
10' generations, then the population groups on either side should exhibit 'edgc
effects' of the same sort that have plagued simulation models of genetic
structure. For example, Endler (1 977) placed local barriers to gene exchange
within a grid of populations and found local edge-effect differentiation along
their borders. Once genetic isolation has occurred, edge-effect differentiation
will become established in the timescale characteristic of local populations,
rather than of regional populations, so only genetic isolation evolving within
the last several thousand generations should escape detection. In the Pieris nupi
group, we have samples of geographically adjacent populations across the
boundary between P. napi and P. bvoniae in the Alps, and the painvise Fstatistics can be dissected to look at only these sets of populations. An edge
effect would appear as higher differentiation between geographically close pairs
across the taxonomic boundary than between pairs within the same taxon, and
the effect would diminish with geographic distance. Comparison of differentiation
within and between these population groups gives no such indication of an
edge effect (Fig. 7), though our between-taxon comparisons are limited at the
closer distances and more sampling is warranted. Nevertheless, even the samples
0.2
I
0
50
100
150
200
Geographic distance (km)
250
Figure 7. Subset of pairwise psT values vs. great-circle distance ( x ) for comparisons involving only
nap; and bymiue. Squares: between taxon; circles: within taxon. Edge effects at a putative boundary
between these taxa would produce higher between-taxon differentiation at closer geographic
distances, but this is not observed.
A. H. PORTER AND H. GEIGER
346
at 40 km are likely to be within a few genetic neighbourhoods of the geographic
boundary, so the pattern is at least consistent with the idea that gene flow is
occurring across their hybrid zone. We do not have samples close enough to
geographic boundaries to test the remaining regions.
Limitations
of genetic
data at regional scales: summary
Patterns at the largest scales are most susceptible to violation of the
equilibrium assumption because regional populations equilibrate very slowly, but
this assumption can be partially tested by looking at patterns on local scales
near regional boundaries. Here the analyses, based on equilibrium assumptions,
make a series of predictions about processes at local scales that may be tested
for consistency. In particular, regions in secondary contact after allopatric
differentiation should show patterns in neutral loci similar to those typical of
hybrid zones (cf. Barton & Gale, 1993), whereas regions having evolved genetic
isolation while in ‘primary contact’ should at least show average divergence at
the boundaries associated with edge effects (cf. Endler, 1977) unless they have
become isolated very recently. The models also predict the average effective
population size (Slatkin, 1993) and average neighbourhood area (above); these
are susceptible to verification from independent ecological studies in many
organisms, including Pieris. They can also be compared to effective population
sizes calculated from the number of alleles in the populations, because these
should also equilibrate on very long time scales. Even though verification of
these predictions does not necessarily imply validation of the equilibrium
assumptions at the regional scale, their verification provides a reasonably tight
circumstantial case, and falsification of any of the predictions can suggest the
nature of the deviation from equilibrium.
Additional aspects
of Pieris
napi group genetics
Variability in local napi group populations (Table 2) ranks among the Drosophila
at the high end of the scale when compared among a broad diversity of taxa
(cf. Nevo, 1978); we found similar patterns in another butterfly (Porter &
Geiger, 1988). In order to maintain this variability in the face of genetic drift,
local effective population sizes must be high. From equation (l), average effective
population sizes on the order of lo3 to lo4 are needed to maintain the genetic
>p >
This
variability we found, assuming a mutation rate of
indicates that napi-group populations have not been through significant bottlenecks
in their recent evolutionary history. Large effective population sizes probably
do not reflect unusually high local population densities, but rather moderate
local densities combined with high vagility. This is evident from the estimate
of the neighbourhood area radius of 3.5 km from the pairwise analysis and is
consistent with our observations of mobility in populations (Porter et al.,
unpublished data). Indeed, this estimate from the pairwise analysis provides a
much-needed link between patterns at regional scales and more easily tested
processes at local scales, and it will be valuable to have independent measures
of neighbourhood area.
The nupi group in Europe has been treated as a superspecies composed of
partially genetically isolated semispecies (Lorkovic, 1962; Bowden, 1972). The
REGIONAL GENE FLOLV
347
reasoning was originally based on reports of occasional hybrid breakdown in
laboratory crosses, differences in the number of satellite chromosomes between
some taxa, and diagnostic morphological and life-history traits (Lorkovic, 1962;
Bowden, 1972). The implication, tacitly invoked by many taxonomists, is that
selection against hybrids imposes strong enough genetic barriers that partial or
even complete genetic isolation has been achieved-this is in opposition to our
inference of strong gene flow between regions. These early studies clearly bear
repetition using appropriate sampling designs, controls and modern laboratory
techniques to verify and quantify the strength of the proposed barriers. Even
at face value, however, these studies described populational and regional averages
of diagnostic traits, and ignored substantial variances-but these large variances
imply that selection imposes only weak barriers at best to regional gene flow.
Theoretical treatments of such conditions show that weak barriers can only
slow gene flow temporarily (Barton & Bengsston, 1986). Thus, the high similarity
at allozyme loci could easily be produced by gene flow, and still not be in
conflict with differences at any loci producing partial hybrid breakdown, nor
with differences in diagnostic traits, provided the differences are maintained by
selection. Taxonomically, of course, any solution depends on which species
concept one subscribes to (cf. Otte & Endler, 1989), and we prefer to defer
discussion of the issue until more is known about underlying processes at
regional boundaries.
ACKNO\VI,EDGER.IENl’S
We were supported in part by grant 31-32463.91 from the Swiss National
Science Foundation and by a Research Challenge grant from BGSU to AHP.
We thank A. Scholl for support and for field samples, and R. Hauser, E.
Meier, G. Thomson, I. Geiger-Bugmann and the numerous people acknowledged
in Geiger and Shapiro (1992) for their help in the field, and L. Frauchiger
and V. Siegfried for assistance during electrophoresis. We also thank A. Scholl
and the reviewers for insightful comments and discussion.
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