Genetic structure in linear habitats
Patterns and processes underlying
population genetic structure in anthropogenic linear habitats:
Four hypothetical scenarios and one case study
DAG Ø. HJERMANN, ROLF ANKER IMS AND SØREN BONDRUP-NIELSEN*
Department of Biology, Division of Zoology, PO Box 1050 Blindern,
N-0316 Oslo, Norway
* University of Arcadia, British Columbia, Canada
Abstract
Linear landscape elements (LLEs) can function both as movement corridors and as habitats. We
focus on the habitat function of LLEs, which in many man-dominated landscapes are important
refuges for wildlife. The main question of this paper is: what happens with the genetic diversity and
structure when most of the original habitat of a plant or animal species is destroyed and reduced to, or
replaced by, a LLE? This depends both on historical (the genetic pattern before LLE was created,
how the LLE was invaded) and current processes (gene flow and genetic drift). Using a numerical
model, we simulate how spatial variation in allozyme frequencies develop in four different scenarios
(which represent different population histories) and at varying gene flow levels and population sizes.
We analyse the resulting spatial genetic variation using FST, spatial autocorrelation of allele
frequencies, and correlation between allele frequencies at different loci. We find that population
history often can influence patterns of spatial genetic variation for at least 50 generations after the
LLE was invaded. Conversely, simple analyses of allele frequencies at two or more loci (e.g.
allozyme data) can yield valuable insight about when and how the species invaded the LLE, and how
much of the spatial genetic pattern that have developed after LLE invasion. As a case study, we
analyse the spatial genetic variation in bush-crickets (the wart-biter Decticus verrucivorus) living in
an LLE, the grassy margins along a major highway in Norway. We cencused the populations as well
as the distribution of habitat along a 54 km stretch of this highway, and sampled animals for genetic
analysis. As genetic markers we used one allozyme locus (malic enzyme, ME) as well as the
coloration (average wing melanism, AWM). We found that the two markers covaried geographically
in spite of being uncorrelated with populations. According to the model, this covariation cannot have
developed after the LLE was invaded, i.e., that these characters covaried genetically also before the
LLE was invaded. We also compared the spatial genetic variation between wart-biters from the onedimensional roadside habitat and wart-biters sampled from a continuous, two-dimensional habitat in
1
Paper VI
the French Alps. The ME differentiation between close neighbouring populations (< 2 km apart) did
not differ between the two habitats, while AWM differentiation, as predicted from genetic theory, was
significantly higher in the one-dimensional habitat.
Introduction
Linear habitats are an important feature of many landscape types, especially in
landscapes dominated by man (e.g., Forman & Godron 1986). These landscape elements are
often referred to as corridors (e.g., Rosenberg 1997), but this term refers more to one of the
functions of these physical entities rather than to the entities themselves. Thus, we will refer
to such structures as "linear landscape elements" (LLEs), most of which can function as
habitats for some species and as movement corridors for other, depending on whether they can
sustain resident populations or whether individuals move from one place to another through
them. A LLE can even have different functions for different individuals of the same species
(Bennett et al. 1994). Zoologists dealing with landscape and metapopulation ecology have to
a large extent focused on the movement function of LLEs, i.e., corridors between wildlife
refuges (e.g., Harrison 1992; Beier 1993; Vermeulen 1994; Dunning et al 1995; Ruefenach &
White 1995; Bowne et al. 1999; Shkedy & Saltz 2000; Danielson & Hubbard 2000). In
contrast, botanists have focused on the habitat function of LLEs, often the detrimental effects
of invading exotic species (e.g., Tyser & Worley 1992; Tabacchi et al. 1996; Planty-Tabacchi
et al. 1996; Greenberg et al. 1997; Oleander et al. 1998; Erskine et al. 1999). However, in
heavily disturbed landscapes, LLEs such as riparian forests (e.g., Knopf & Samson 1994;
Bratton et al. 1994; Spackman & Hughes 1995; Burbrink et al. 1998) and roadside habitats
(e.g., Major et al. 1999) can be important habitats of a wide range of wildlife (including
plants), and can act as genetic reservoirs for species threatened by loss of genetic variation.
In this paper, we focus on the habitat function of LLEs that result from human
activities. We define LLEs to include both linear habitats created by reduction of a formerly
more widespread, two-dimensional habitat type (e.g., forest remnants along rivers and lakes),
or newly created habitat (e.g., roadsides). We seek the answer of the following question: what
happens with the genetic diversity and structure when most of the original habitat of a plant or
animal species is destroyed and reduced to, or replaced by, a linear habitat? The answer
depends on both historical and current processes. Historically, it will depend on the genetic
pattern before the landscape changed and how the LLE was colonised. Current processes
include gene flow and drift among populations along the LLE. With respect to historical
2
Genetic structure in linear habitats
processes, a crucial question is whether we can reconstruct how the genetic pattern was before
the landscape changed, and how the LLE was colonised, based on the current pattern of allele
frequencies. The answer to this question hinges on to which degree it is possible to separate
historic patterns from patterns generated contemporary processes (Templeton et al. 1995).
Spatial genetic variation of linear populations or linear arrays of populations has
often been treated in theoretical papers (e.g., Kimura & Weiss 1964; Kimura & Maruyama
1971, Rousset 1997). The theoretical works, however, tend to ignore the initial conditions,
i.e., they assume that gene frequencies are uniform or randomly distributed in space at the
time populations are established. Also, there are other factors that may add to the theoretic
effects of habitat dimensionality on genetic variation. For instance, the density of individuals
can be both higher or lower in linear compared to non-linear habitats (e.g., Fauske et al. 1997;
Major et al. 1999), and linearity may or may not increase dispersal (e.g., Andreassen et al.
1996). In spite of the many models of evolution in LLEs, there are very few empirical papers
that focus on genetic structure in LLEs, especially with a focus on how habitat dimensionality
can affect genetic variation. Thus, theory has generally remained untested on this issue.
This paper consists of two parts.
First, we present four scenarios of how
anthropogenic LLEs might be created and how a species may establish populations along an
LLE. To examine how genetic variation may develop in each scenario, we use a simulation
model to examine how allele frequencies at two loci may change as a function of local
population size and the level of migration (assumed to be of the stepping-stone type) between
populations. In the second part, we analyse the spatial genetic variation in a species of bushcricket (the wart-biter Decticus verrucivorus) that lives in the narrow grassy strip along a
highway in Norway. The observed pattern of genetic variation in this LLE is compared with
the simulation results and that of wart-biters living in a continuous non-linear habitat in the
French Alps.
Theory
Ecological scenarios
The creation and colonization of LLEs may come about from different processes
(Fig. 1). The LLE may either be newly created habitat (Fig. 1a,b; e.g., roadside habitat
through a field, or deciduous vegetation in a power line corridor through a conifer forest) or a
linear remnant after destruction of a once widespread habitat (Fig. 1c; e.g., remnants of forest
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A
B
C
Figure 1. Four scenarios of establishment of LLEs and LLE populations. See text for explanation.
between a clearcut and a river). In the first case, LLE populations are founded by dispersers.
In the latter case, populations at least in part, stem from the animals that happened to live
there when the rest of the habitat was destroyed. The animals founding LLE populations may
immigrate more or less perpendicularly onto the LLE (Fig. 1a), along the LLE (Fig. 1b), or in
a combination of the two. In the resulting LLE, the species may be widespread throughout, or
may form more or less distinct populations separated by stretches of unsuitable habitat.
In any case, the history of the corridor populations is likely to be reflected in the
spatial genetic variation (SGV) among the corridor populations. To illustrate the range of
possibilities, we present four scenarios which represent extreme situations or caricatures.
1.
The source population is widespread and has negligible SGV. After general habitat
destruction, small populations are established along the LLE. SGV among LLE
populations arises is a result of genetic drift and limited dispersal of individuals between
neighbouring populations along the LLE; thus, a balance is reached between genetic drift
and migration. According to Wright’s classic model of isolation by distance, we expect
that FST increases with time and spatial autocorrelation in allele frequencies. Fig. 1c may
illustrate this scenario.
2.
There is a gradient pattern in the SGV of the source population, i.e., the allele frequency of
a given allele is gradually decreasing/increasing from one end of the region to the other.
This gradient may originate from an isolation-by-distance model or from a hybrid zone.
LLE populations are established by dispersing more or less perpendicularly onto the LLE.
At the time of establishment, the spatial pattern of genetic variation generally corresponds
to that of the original populations. Fig. 1a or 1c may illustrate this scenario.
4
Genetic structure in linear habitats
3.
The source population is subdivided with a low migration rate between subpopulations,
and long-distance migration is as common as migration between neighbouring populations
(the island model). LLE populations are established in the same way as in Scenario 2. As
a result allele frequencies among populations diverge, but without any specific geographic
pattern. Fig. 1a may illustrate this scenario.
4.
There are source populations only at the ends of the LLE at the time of LLE creation, and
allele frequencies differ between the two sources. LLE populations are established by
invasion along the LLE (Fig. 1b). Assuming that colonization of the LLE is relatively
rapid, a steep cline or a "step" in allele frequencies is likely to develop somewhere around
the middle of the LLE.
We used simulation models to explore the genetic consequences of these scenarios.
The simulations started at the time of LLE establishment. We explored three cases where
SGV is present when populations are founded (reflecting SGV in the two-dimensional source
habitat), and one case where it is absent.
In addition, we varied population sizes and
migration rates.
The model
The model represented 20 linearly arranged patches/populations. We followed two
loci (A and B) with two alleles each (A1,A2; B1,B2). We assumed random recombination
between the two loci (e.g., they may be on different chromosomes), and we also assumed that
we can ignore effects of mutation. The allele frequencies of A1 and B1 were denoted pA and
pB, respectively. Generations were non-overlapping and the number of individuals in each
population was assumed to be stable. Mating was random and formed the stochastic element
in the model, while we assumed that gene flow was deterministic.
We ran models with four different patterns of SGV at establishment of populations
in the LLE, which we will call Constant, Gradient, Random, and Step, corresponding to
scenario 1-4 above (Fig. 2).
In Constant we assumed no spatial variation in the allele
frequencies in the ancestral population(s), so that pA = pB = 0.5 in all 20 populations at
establishment. In Gradient we assumed that allele frequencies changed gradually in space at
establishment, from pA = pB = 0.3 in one end of the LLE to pA = pB = 0.7 in the other. In
Random, the initial variation in allele frequencies was the same as in Gradient, but pA and pB
varied independently of each other and without any geographical pattern. In Step we let the
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Paper VI
0,8
Constant
0,5
0,2
0,8
G radie nt
0,5
0,2
0,8
Random
0,5
0,2
0,8
0,5
Ste p
0,2
0
5
10
15
20
P opula tion num be r a long LLE
Figure 2. Outline of the different patterns of spatial genetic variation (SPV) at LLE establishment in
the simulation study. The horizontal axis represent space along the LLE, while the vertical axes
represents pA and pB (the allele frequencies of A1 and B1) for each of the twenty populations along the
LLE. The lines show initial SPV patterns for each of the scenarios Constant, Gradient, Random and
Step (see text for further explanation). In the case of Random, pA and pB is shown with separate lines.
In the case of the three other scenarios, pA = pB and each line thus represent both allele frequencies.
populations in one half of the LLE start with pA = pB = 0.4 and the populations in the other
half start with pA = pB = 0.6.
For each pattern of initial SGV, we ran models where we varied the population size
N of the LLE
populations (15 or 60) and migration rate (m) between neighbouring
populations (15 different values from 0 to 0.20). For simplicity, migration was supposed to
occur as gamete migration among neighbouring populations (e.g., pollen spread). For each
mating bout, 1-m of the gamete pool in populations with two neighbours consisted of gametes
from the population itself, while its neighbours contributed with m of the gamete pool (m/2
from each neighbour). Then , N new individuals were formed by picking two gametes at
6
Genetic structure in linear habitats
random from the gamete pool N times. Those N new individuals completely replaced the
former generation (i.e., generations did not overlap). For the two populations at each end, 1(m/2) of the gamete pool comes from its own individuals. Thus, there was no stochastic
element in the migration process.
We ran 30 simulations for each combination of initial condition, N and m. For each
generation, we calculated FST for each locus following Weir & Cockerham (1984). For
generation 5,10, 20 and 50 we also calculated the correlation between pA and pB for each
generation, the spatial autocorrelation for each allele for lag = 1 through 5, as well as the
cross-correlation between pA and spatially lagged values of pB and vice versa. We used
Spearman’s correlation for all correlations. To summarise the auto- and crosscorrelation
results, we used the correlation coefficient at lag = 1 as well as the slope of a linear regression
of the correlation coefficient vs lag.
Simulation results
Figure 3 sum up the main results of the simulations. The overall FST (Fig. 3, left
column) is the best-known of the statistics presented. Early in the life of the LLE populations,
FST was naturally strongly influenced by the genetic pattern at initiation, but also by the size of
the populations. As time went by, FST increased, especially for low migration rates and no
initial SGV. After 50 generations, the initial presence of a gradient had little influence
compared to population size and migration rate.
The plots of autocorrelation at lag = 1 (Fig. 3, middle column) reflects that at the
start of the simulations, autocorrelation was positive for the simulations initiated with a
gradient (especially with large populations), and zero for the other types of initial SGV. As
time goes by, genetic drift served to reduce autocorrelation in the Gradient simulations with
low migration rate, while migration led to autocorrelation in Constant, Random, and Step, the
faster the higher migration rate. After 50 generations, autocorrelation was neither influenced
by initial SGV or population size, while migration rate (especially below 0.05) is very
important. The slope of the autocorrelation function (not shown) was largely a mirror image
of the autocorrelation coefficient at lag = 1.
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Paper VI
8
Genetic structure in linear habitats
Figure 3 (previous page). Results of the simulation study. The figures show three different measures
of genetic structure (from left to right: FST, spatial autocorrelation, and correlation between loci) at
different times after populations are established in the LLE (from top to bottom: 5, 10, 20 and 50
generations after establishment). Within each figure, each line represent one combination of scenario
and population size. The secenarios are Constant (open circles), Gradient (filled circles), Random
(open triangles) and Step (filled triangles); population size is N = 15 (unbroken lines) or 60 (broken
lines). On the horizontal axis is the migration rate (the proportion of immigrants from neighbouring
populations). FST measures overall genetic differenatiaton between populations. The spatial
autocorrelation is the correlation (Spearmans rank correlation coefficient) in allele frequencies
between neighbouring populations (lag = 1; averaged for the two loci). The correlation between loci is
correlation in allele frequencies between the two loci, measuerd by Spearmans rank correlation
coefficient. See text for more details.
The correlation coefficient between the loci (Fig. 3, right column) was positive only
when there was a gradient in the initial allele frequencies. In that case correlation persisted for
a long time, especially for large population sizes. For Gradient with K = 60, correlations
declined a bit when migration rate went below 0.05. Crosscorrelation at lag = 1 is not shown
because it largely resembled the ordinary correlation, and the slope of the autocorrelation
function resembled a mirror image of the correlation coefficient.
(In the case that the
geographic gradients of allele frequency goes in opposite directions for the two loci,
correlation will of course be negative, while the slope will be positive.)
As we see, the different statistics can provide information on different aspects of the
history and ecology of the linear habitat populations. Except for the "step" simulations,
migration rate influences overall FST and autocorrelation; after 20 generations, the latter
statistic is determined by migration rate alone. Population size has a distinct effect on FST
when some time has passed. A genetic gradient in the founding populations can be traced as a
correlation between the allele frequencies; this correlation is persistent even after 50
generations, in contrast to FST. A "step" in the allele frequencies will tend to lead to very high
FST values which will be little influenced by neither population size or migration rate, which is
hardly influenced by the initial conditions when more than 10 generations has passed.
Case study: Wart-biters along a highway
Study organism
The wart-biter (Decticus verrucivorus L.) is a relatively large bush-cricket
(Orthoptera: Tettigoniidae) found in meadows and grasslands in continental Europe and in the
warmer parts of England and Scandinavia. In Norway it is restricted to the lowlands in the
South-eastern part of the country, and it has become much less common the last decades
9
Paper VI
because it requires relatively low, unfertilised meadow vegetation, a type of habitat that has
become relatively uncommon in this part of the country. However, it can also live in the
grassy verges along major roads, as long as this vegetation is kept down by cutting rather than
by using herbicides. Although the species is not wingless, it is effectively almost flightless: it
flies only when disturbed, and then only up to five meters; longer flights are extremely
uncommon (Ander 1947).
In Norway it occurs in relatively low densities.
We have
previously shown that the pattern of presence/absence in small habitat patches largely fits a
metapopulation pattern and that migration capacity is fairly restricted (Hjermann & Ims 1996).
Methods
Landscapes, sampling and surveys
The main study area was a 55 km long stretch of the major highway (E-18) that runs
south-westwards from Oslo along the coast. The north end of the stretch was just south of
S a m pling de sign from highw a y
roa dside s
0
10
20
30
40
50
Inte nsive ly sa m ple d highw a y stre tch
37
38
39
40
41
42
Sa m pling de sign in the continuous la ndsca pe (the Fre nch Alps)
0
1
2
3
4
5
6
Figure 4. Outline of sampling areas of this study. The roadside habitat was not completely straight in
reality. In the case of the roadside, the thin inner lines above and below the km-line represent habitat
on the east and west side of the road, respectively, and the thick outer lines show where male wartbiters were observed. The crosses above the lines show where we sampled animals for analysis
(without regard to which side of the road we sampled).
10
Genetic structure in linear habitats
Holmestrand town (= 0 km) and the south end was at a tunnel entrance just before Larvik
town (= 54.8 km). The stretch runs through one of the most intensively exploited agricultural
landscapes in Norway, although there is a substantial proportion of forest and residential areas
as well. Except for the verges of the main roads, almost no parts of the present landscape is
suitable for the wart-biter. A few decades ago, however, meadows suitable for the species
probably covered a substantial part of the landscape. Large parts of the road we surveyed has
been built since 1980. Thus, the species has in part shifted from meadows to roadside
habitats.
The habitat along both sides of the road was surveyed. For each 100 m interval, we
recorded the number of singing males for each 100m interval and for each side of the road. In
addition, we recorded presence of major dispersal barriers (such as rivers or major crossing
roads), and we categorised each side of the road into one of the following categories:
grass/meadow along open habitats (such as fields), forest or cliffs/rock.
In the case of
grass/meadow, we also noted whether the road verge was flat or sloped towards or from the
road, and whether it was narrow or broad (> 3 m). The categorisation of the habitat was done
by one of the authors (DØH) that had some experience with wart-biter habitat requirements in
general, but no experience of the distribution of wart-biters along this road. Both the habitat
survey and the observation of animals was achieved by driving by car at moderate speed along
the road. The surveys of singing males were done during optimal singing conditions (sunny
days around 9 p.m. to noon); animals were counted three times on the western side of the road
and four times on the eastern side.
In July-August 1997 and 1998, wart-biters were sampled at 21 locations along this
transect (Fig. 4a). In addition, wart-biters were sampled at two more locations further north
on the same road (15 and 45 km north of the transect start, respectively). We sampled on both
sides of the road in 13 of these locations (wart-biters were not always present at both sides).
Of the 21 locations, we allocated eight locations to a 4.1 km stretch (km 37.4 - 41.5; Fig. 4b)
that was almost continuously populated by wart-biters.
For comparison with the latter
subsegment of the road, we also obtained a sample of wart-biters in an elongated, 5.2 km long
area at an altitude of 2000-2200 m in the French Alps (located 3 km north of the village
Versoye-les-Granges north of Seez, close to the French-Italian border). In this sampling area,
the entire landscape is a suitable wart-biter habitat with high densities of the species. Wartbiters were sampled from eight points with a range of 5.2 km (Fig. 4c) in July-August 1998.
11
Paper VI
[For simplicity, we will throughout this paper refer to wart-biters from a sampling
site as a population, although we postpone to find out to which degree they really are separate
populations in the "population genetic" sense of the word.]
Spatial distribution of wart-biters in the surveyed LLE
For simple analyses of the numbers of observed wart-biters and the number of
segments with wart-biters on each side, we used the average number per survey (four surveys
on the eastern side, three on the western).
Since the LLE may not be completely invaded by wart-biters yet, we analysed the
abundance of males along the road using correlation analyses (Proc Arima in SAS, SAS
Institute 1996). Since we were most interested in the spatial variation of wart-biters that could
not be attributed to the distribution of habitat, we calculated the mean numbers of males per
100 m segment for roadside classified as habitat and non-habitat, respectively, and used the
residuals from the mean in autocorrelation analyses "corrected" for presence of habitat. We
ran three kinds of autocorrelation analyses on the residual abundance. First, we calculated
simple and partial autocorrelation on each side of the road separately. Second, we calculated
the cross-correlation between opposite sides of the road, i.e., the correlation between the
corrected wart-biter abundance one side and the corrected abundance some distance north or
south on the other side. In the third analysis, we examined abundance patterns on a larger
scale. We divided the road in eleven intervals: 0-5 km, 5-10 km, …, 45-50 km, 50-54.8 km,
and analysed the differences between these stretches by incorporating ten dummy variables
that represented the eleven road intervals (i.e., contrasts between the first interval and each of
the other) into a first-order autocorrelation model. In such a model, the estimated parameters
for the dummy variables tell us whether there are differences in abundance between the eleven
intervals that can not be attributed to distribution of habitat or the autocorrelation between
proximate 100 m intervals. If wart-biters invade the LLE from a few points along it, and
invasion is not complete, we expect such differences.
Genetics: Laboratory and statistical methods
The live-caught wart-biters were killed by freezing them at -20 °C. Within 48 hours,
the animals were moved to a -80 °C freezer. We recorded each animal's sex and the wing
melanism (i.e., the amount of black pigmentation on the wings), which was assessed on a
scale from 0 (no black) to 5 (almost entirely black). The animals were homogenised at 0 °C
12
Genetic structure in linear habitats
after removing the crop, the wings and the hind feet. After initial trials with ca. 25 enzymes,
we found that only malic enzyme (ME) returned suitable results. We found two discernible
alleles of this enzyme; we will call the slowest-moving allele 1 and the other allele 2. We use
pi to denote the allele frequency of allele 1 in population number i.
In the subsequent analyses which will be described below, we used each sample’s
average wing melanism (AWM) as a genetic character independent of the ME alleles. Thus,
we assumed as that a substantial portion of the variation in wing melanism could be attributed
to genetic differences, and in autocorrelation analyses we used AWM as it was a gene
frequency. This was taken as a a working hypothesis, since we know no studies of the
heritability of melanism in this species. Among grasshoppers and crickets as a whole, there
are species where coloration is primarily being controlled by developmental conditions
(acridoid grasshoppers: Rowell 1971, Colvin and Cooter 1995, Sword et al. 2000; bushcrickets: Lymbery 1992) and other species where coloration is genetically controlled
(groundhoppers: Forsman 1999a, 1999b; bush-crickets: Oda and Ishi 1998; wetas: King et al.
1996, Morgan-Richards and Gibbs 1996). Cherrill & Brown (1991) noted that melanism
appears to vary geographically in this species, but this is not inconsistent with melanism being
environmentally determined. We tested the other part of the assumption, that wing melanism
and ME genotype are independent (i.e., not genetically or physiologically linked), using a
logistic model. The response variable was number of allele 1 in each individual (as the
outcome of a binomial process with n = 2) and the predictor variables were wing coloration
and population (the latter variable was included to remove the effect of between-population
correlation). The outcome of a type III likelihood ratio test (using Proc Genmod, SAS) was
that wing coloration had no effect on the ME genotype, i.e. that these two variables were not
correlated within the Norwegian populations (χ2 = 0.02, P = 0.90).
We used Genepop 3.1 (Raymond & Rousset 1995) to analyse genetic variation based
on ME genotype. We calculated genic differentiation and FST (following Weir & Cockerham
1984) for both the entire samples and for pairwise locations within each sample. If genetic
variation was structured geographically as expected from the "isolation by distance" model,
we expect a linear relationship between FST/(1-FST) and ln(distance) of population pairs
(Rousset 1997). In Genepop, this is tested with a Mantel test, a permutation procedure
(Mantel 1967). We tested this using physical distance (along the road) for the highway
sample including the two locations north of the surveyed stretch. For the surveyed stretch, we
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Paper VI
also did the same test using three other distance measures, based on the assumption that forest
and perhaps cliffs are barriers to dispersal: "forest distance" (distance with forest on both sides
of the road); "forest + cliff distance" (distance with forest or cliffs on both sides of the road),
and "non-habitat distance" (distance with no habitat on either side of the road)). We did the
same tests with AWM, replacing FST with absolute difference in AWM.
To be able to compare the spatial genetic pattern of the wart-biters with the results of
the simulation model (see above), we performed correlation analyses of the genetic structuring
of wart-biters following the same main scheme as used for the simulation results. We tested
whether allele frequency (p) was correlated with average wing melanism (AWM) for each
population. Autocorrelation for both p and AWM was analysed in two ways: by correlating
locations separated by a certain number of locations, and by correlating locations separated by
a certain distance in kilometers. For the first type of analysis on the highway sample, we
pooled the 37.4, 37.7 and 38.5 km locations and the 39.8, 40.2, 40.9, 41.2 and 41.5 km
locations in order to reduced the variance in between-location distance.
Ordering the
locations after their order in the transect (i = 1 to 17), we also tested whether p was
autocorrelated, i.e., whether pi was correlated with pi -lag, where lag = 1, 2,…7 and i = 1+lag to
23. The same way, we tested whether AWM was autocorrelated. We also calculated crosscorrelations between p and AWM, i.e. the correlation between pi and AWMi -lag and between
AWMi and pi -lag. In the second approach, we analysed correlation between locations separated
by <5 km, 5-10 km, 10-20 km 20-30 km, 30-40 km and 40-60 km.
We tested whether allele frequencies differed between the east and west sides of the road
using a logistic regression of the allele frequencies with location and side and their interaction
as predictor variables. Using the same predictor variables in a two-way Anova, we tested
whether AWM differed between the sides of the road.
Results
Spatial distribution
We made altogether 625 observations of singing males in 259 road segments (24 %
of the 2 x 548 segments; Fig. 4a, Tab. 1). 15 % of the observations were made in segments
we had classified as non-habitat for wart-biters. We observed wart-biters in a significantly
higher fraction of the segments on the eastern than on the western side of the road. The
reason for this was that higher fraction of the habitat segments on the eastern side of the road
14
Genetic structure in linear habitats
Table 1. Some basic data from the survey of wart-biter (Decticus verrucivorus, D.v.) and its habitat
Norwegian highway, including tests of differences between the east and west side of the road. Tests
were either Pearson goodness-of-fit tests of independence (those reporting χ2) or Mann-Whitney U
tests (those reporting Z, which refers to the standard normal distribution uinder the null hypothesis).
West
East
Total
548
548
1096
classified as habitat
377
360
737
% classified as habitat
69
66
67
83.7
93.5
177.2
in habitat segments
66.3
84.5
150.8
Segments with D.v. (total)
110
149
259
χ2df=1 = 7.69 **
Average presence of D.v. §
0.112
0.125
0.119
Z = -2.09 *
habitat segments only
0.128
0.171
0.149
Z = -3.26 ***
non-habitat segments only
0.076
0.037
0.056
Z = -1.50
% non-habitat of D.v. segments
21
12
17
χ2df=1 = 3.03 (*)
0.153
0.171
0.162
Z = -2.20 *
0.176
0.235
0.205
Z = -3.39 ***
0.101
0.048
0.075
Z = -1.48
0.771
0.645
0.695
Z = -2.96 **
Number of 100 m segments
Number of D.v. observed per survey
No. of D.v. per segment per survey
in all habitat segments
in all non-habitat segments
in habitat segments with D.v.
(a)
†
in1 non-habitat segments with D.v. † 0.722
(b)
0.500
Tests
χ2df=1 = 1.19
0.627
Z = -2.46 *
0,4
W es t, s im ple autocorrelation
( )
Corre lation coe fficie nt
C orre lation coe fficie nt
W es t, partial autocorrelation
0,8
* P < 0.10,
* P < 0.05,
** P < 0.01, *** P < 0.001
0,3
East, sim ple autocorrelation
The numbers
show
the
probability of observing D.v. in a segment on a given survey
East, partial autoc orrelation
0,6
†
With D.v. on one or more surveys
§
0,4
0,2
were occupied
by wart-biters (Tab. 1). However, the two sides did not differ in the fraction of
0,2
0,1
occupied non-habitat segments, nor in the numbers of males observed in occupied segments
0
(Tab. 1).
0
1
2
3
Lag (km)
-0,2
0
-3
-2
-1
0
1
2
3
Lag (km)corrected for habitat
Using the residual numbers of wart-biter males (i.e., numbers
distribution), we found that the abundance of observed wart-biters were spatially
(c)
2
autocorrelated on both sides of the road. On the eastern side, segments up to 2.1 km apart
1,5
Re lativ e abundance
were 1significantly correlated, while western segments further apart than 600 m were
0,5
East
uncorrelated
(Fig. 5a). In the second correlation
analyses, we found that the residual number
W es t
0
of wart-biters were quite strongly correlated between the eastern and western sides (r = 0.35),
-0,5
and the
-1 corrected number of wart-biters in one segment also correlated with segments up to
-1,5 away on the other side (Fig. 5b). In the last analysis, where we looked for differences
2.2 km
0
10
20
30
40
D istance along transe ct (km)
50
15
Figure 5. Autocorrelation of wart-biter abundance. (a) for each roadside. (b) Cross-correlation
between roadsides for different spatial lags (c) Abundance in 5 km segments corrected for
autocorrelation.
Paper VI
in wart-biter abundance on a larger scale, we found that the abundance of wart-biters was
substantially higher in the 30-45 km compared to the rest of the LLE (Fig. 5c). Especially, the
abundance on the eastern side in the 35-45 km stretch was very high both compared to the rest
of the road and compared to the same stretch on the western side. For the rest of the road,
densities appeared similar between the two sides.
Patterns of allele frequencies and wing melanism
The ME genotype was successfully recorded for 357 animals along the highway (of
1
5
(a) 146 were caught in the intensively sampled stretch). There
which
was some evidence of
p
heterozygote
deficit
AW M(Fis = 0.12, P = 0.014) and good evidence for genic differentiation
0,8
4
between populations (Fst = 0.031, P = 0.005). The allele frequency of allele 1 (p) varied from
0,6
p
3
AWM
0.2 (at -45 km, n = 5) to 0.857 (at 41.2 km, n = 14) (Fig. 6a). The Mantel test for isolation by
distance
0,4 (using FST/(1-FST) and loge(distance)) did not yield good evidence that gene
differentiation between pairs of populations increases with distance (one-sided test,
2
0,2
P = 0.088). The same test ran using "forest distance", "forest+cliff distance" and "non-habitat
distance"0 (for the 21 populations within the surveyed part of the 1transect) only resulted in
-50 -40
-20P =-10
20
30
40
50 The
60 allele frequencies did not
higher P-values
(P =-300.26,
0.30 0and 10
P = 0.31,
respectively).
Dista nce a long tra nse ct (km )
differ between the east and west sides of the road (location*side interaction: χ2 = 14.27, df =
(b)
1
(c)
5
1
5
12, P = 0.28; side: χ2 = 1.31, df = 1, P = 0.25).
Within the intensively
sampled stretch (Fig.
4b), 0there
might have been a deficit of heterozygotes
(Fis = 0.12, P = 0.07), but there was no
,8
0,8
4
4
evidence for genic differentiation between populations (Fig. 6b; Fst = 0.0092, P = 0.17) and no
0 ,6
AW M
0 ,4
3
p
p
3
AW M
0,6
0,4
2
0 ,2
2
0,2
p
p
AWM
0
AWM
1
37
38
39
40
41
42
Dis ta nc e along tra ns ec t (k m )
0
1
0 1 2 3 4 5 6 7 8 9
Dis ta nc e along tra ns ec t (k m )
Figure 6. Allele frequencies (p) of allele 1 of the ME enzyme and average wing melanism (AWM)
along the Norwegian transect (a), the Norwegian subtransect in detail (b) and along the French
transect (c).
16
Genetic structure in linear habitats
Table 2. Gene frequencies (p) and average wing melanism (AWM) for each sampling location along
the highway. Km denotes distance from the start of the road survey (the two "negative" sampling
points were located outside the surveys strecth) and N denotes the sample size. The last four columns
relate to differences between pairs of successive sampling locations: distance between locations, FST,
the absolute difference in AWM (∆ AWM) and a P-value that summarizes the significance tests of FST
and ∆ AWM.
Relative to next sampling point along road
Km
N
p
AWM
Km
FST §
-45
5
0.20
2.60
30
0,169
-15
29
0.57
2.72
19.8
4.8
4
0.25
2.25
5.9
7
0.71
7.4
21
11.4
'
*
AWM †
Summarized P #
0.12
0,72
0,099
0.47
0,26
1.1
0,235
0.18
0,74
2.43
1.5
-0,020
0.43
0,77
0.60
2.00
4
-0,028
0.40
1,2
10
0.55
1.60
2.4
0,088
2.07
** 0,13
13.8
3
0.83
3.67
3.4
-0,067
1.17
1,26
17.2
16
0.72
2.50
6.1
-0,019
1.14
** 0,58
23.3
12
0.79
3.64
10.1
-0,039
0.03
3,79
33.4
9
0.78
3.67
4
0,076
1.01
37.4
24
0.54
2.65
0.3
0,012
0.53
37.7
29
0.67
3.18
0.8
-0,016
0.55
38.5
20
0.60
2.63
1.3
-0,017
0.49
0,54
39.8
24
0.67
3.13
0.4
-0,034
0.21
1,81
40.2
11
0.73
3.33
0.7
-0,063
0.71
1,29
40.9
8
0.69
2.63
0.3
0,036
0.52
0,26
41.2
14
0.86
3.14
0.3
0,165
0.43
0,09
41.5
16
0.56
2.71
1.3
-0,026
0.10
2,53
42.8
13
0.62
2.62
2.1
0,117
0.62
0,03
44.9
11
0.32
3.23
3.2
-0,011
0.66
0,24
48.1
7
0.50
2.57
0.6
0,033
0.10
1,08
48.7
25
0.70
2.67
6
0,035
0.13
0,52
54.7
39
0.54
2.54
-
-
-
-
*
*
0,014
*
0,09
*
0,32
*
* P < 0.05, ** P < 0.01, *** P < 0.001
§ The indications of statistical significance are results of Fisher exact tests on allele frequencies
† The indications of statistical significance are results of t-tests
# Summarized P = [P(FST) + P(∆ AWM)]2
17
Paper VI
evidence that gene differentiation increased with distance (P = 0.43). The only pairs of
successive sample points that had significantly different values of p was -45 and -15 km and
41.2 and 41.5 km (Tab. 2; note the small spatial distance of the latter pair).
In the sample from the French Alps (Fig. 6c; 186 animals), there was no significant
heterozygote deficit (Fis = -0.033, P = 0.54), and we found no evidence of genetic
differentiation (Fst = -0.0021, P = 0.41).
p varied from 0.66 to 0.85 (Fig. 6c), with no
apparent structure along the transect (Mantel test for isolation by distance: P=0.67).
Comparing difference in allele frequencies among neighbouring populations that lie < 2 km
from each other, the average pairwise normalized FST (FST /[1 + FST]) was 0.001 (SE 0.006;
N=15) in the French sample and 0.023 (SE 0.023; N=11) in the Norwegian subsample. When
correcting for distance (using Ancova), this difference was not significant (F1,23 = 0.93, P =
0.34). Thus, there is no indication that genetic distance (relative to physical distance) differs
between the continuous habitat in the French Alps and the intensively sampled stretch of the
Norwegian highway. For average wing melanism (AWM), we find that the absolute difference
in AWM for populations <2 km apart was 0.28 (SE 0.05) in the French sample and 0.45 (SE
0.07) in the Norwegian subsample. This difference was statistically somewhat significant
when we corrected for distance (F1,23 = 5.47, P = 0.028).
Average wing melanism (AWM) and correlations between AWM and allele frequencies (p)
The average wing melanism (AWM) varied from around 2 to 3.5 (Fig. 6a). The
Norwegian animals were significantly darker than the French (Anova, F22,329 = 3.05, P <
0.0001). Within the Norwegian transect, there was good evidence that p was positively
correlated with AWM (Spearman’s rho = 0.52, p = 0.011, Fig. 6a, b). The change in p and
AWM between consecutive populations was correlated as well (Spearman’s rho = 0.49, p =
0.019), especially for the 15 populations from km 4.8 through km 41.5 (Spearman’s rho =
0.86, P < 0.0001). However, when testing which pairs of successive sample points that were
significantly different with respect to p and AWM, respectively, different sets of pairs resulted
(Tab. 2). There were quite large differences with regard to both p and AWM between the pairs
33.4-37.4 km and 42.8-44.9 km.
The two variables did not correlate in the French transect (Spearman’s rho = -0.31, P
= 0.46, Fig. 6c).
18
Genetic structure in linear habitats
Autocorrelation of p and AWM, and cross-correlation between p and AWM
Correlating populations separated by a number of populations along the road, p
might have had a tendency to be positively correlated for lag = 1 through 3, and negatively
correlated thereafter. However, the only correlations significant with P < 0.05 were with lag =
6 and 7 (Fig. 7a). AWM showed generally the same tendencies, but in this case no correlations
were significant at the 5 % level (Fig. 7a). Correlating populations separated by a number of
kilometres instead, there was is no tendency of autocorrelation of p at all, while AWM shows a
similar response as in the first approach, but with the only significant correlation being a
negative correlation at a lag of 20-30 km.
There were also substantial cross-correlation between p and AWM along the road
(Fig. 7b). The correlation between pi and AWMi-lag seemed to decline to a minimum and
thereafter rise again, being significantly negatively correlated at lag = 4 populations or 10-20
km (Fig. 7b). AWMi was positively correlated with pi -lag at lag = 2 or 3 populations; the same
pattern could be traced when physical distance was used as lag, but much weaker and
uncertain.
(a)
(b)
p(i) vs . AWM(i-lag)
p
0,8
0,8
AWM(i) vs . p(i-lag)
0,6
0,6
0,4
0,4
0,2
0
-0,2
0
2
4
6
8
Spe a rm a n’s r
S pe a rm a n’s r
AWM
0,2
0
-0,2
-0,4
-0,4
-0,6
-0,6
-0,8
0
2
4
6
-0,8
La g
La g
Figure 7. (a) Autocorrelation for allele frequency (p) and melanism (AWM) and in the Norwegian
transect. (b) Cross-correlation between allele frequency (p) and melanism (AWM). In both panels,
"lag" (on the horizontal axis) is number of populations, and Spearman’s correlation coefficient was
used. The eight populations in the Norwegian subtransect were pooled to two populations (see
Methods). Correlation values above/below broken lines are statistically significant (P<0.05).
19
8
Paper VI
Discussion
The use of correlation techniques in the study of spatial genetic variation has been
fairly well studied by simulation studies (reviewed by, e.g., Epperson 1993). However, the
simulation presented here differs from most other such studies in a number of respects. First,
we emphasise the influence of nonrandom gene frequency distributions at population
establishment.
It is a more usual approach to initiate populations with some "null"
distribution of allele frequencies, i.e., a random or constant distribution.
Second, we
emphasise the situation from the time of colonization of the linear habitat and for a relatively
short period thereafter. Commonly, simulations are run for at least a thousand generations and
focus is often on the situation several hundreds of generations after initiation, when some kind
of equilibrium has been reached. Third, we have dealt with two loci rather than one, and
explored the covariation between their allele frequencies.
This is not common, simply
because two loci are not expected to correlate a lot if it is assumed that they are unlinked and
independently distributed initially (but see Epperson 1993). All of these points reflect that we
focus on anthropogenic linear habitats. Most of these landscape elements have been created
fairly recently (although the habitat itself may be ancient, as in Fig. 1c). The individuals that
established in these habitats were not necessarily a random sample of a single source
population; they just as likely came from a variety of widely spaced source populations that
may have displayed substantial geographic genetic variation.
Kimura & Weiss (1964) analysed mathematically a model quite similar to ours;
populations in a one-dimensional array that only exchange individuals with adjacent
populations at a rate of m/2 per generation. They found that at equilibrium, FST was related to
Nm (the product of population size and migration rate) by the function FST = 1/[4N(2mµ)0.5 +
1], where µ is the mutation rate. One prediction from this model is that genetic differentiation
relative to distance is expected to be larger in linear than in two-dimensional habitats (e.g.,
Wright’s island model where all populations exchange individuals). Another prediction is that
in the absence of mutation, FST approaches 1, independently of migration rate as the mutation
rate approaches zero. This means that if the system is initiated with FST = 0, FST will increase
until it is counterbalanced by the effects of mutation. (It thereby differs from the island
model, where FST = 1/[4N(m+µ) + 1]). This is in accordance with our model (where we
20
Genetic structure in linear habitats
21
Paper VI
assume zero mutation); we find FST to be increasing steadily through time for all migration
rates.
A main result of the simulations is that if the gene frequencies of two loci co-vary
geographically when populations are initiated, the correlation persists for as 50 generations
after initiation even when the loci are completely unlinked and the level of migration is quite
high. A just as striking result is that neither the Step or Random models can be distinguished
from each other or the Constant model (except for differences in FST).
If the parameters are fairly well known, simulations can be used to predict roughly
how the spatial genetic pattern will evolve in a linear habitat that is currently under
establishment. As linear habitats become increasingly important habitats many species, they
may also become vital for the conservation of genetic diversity within species.
Such
conservation depends on keeping an optimal balance between genetic drift and gene flow - too
much gene flow may eradicate differences between locally adapted genotypes, while too little
gene flow may cause inbreeding depression.
However, these simulations may have greater practical importance as a tool that
potentially can help us make inferences about historical and contemporary processes. In Table
3 we have indicated some ways to combine known facts of the populations with simple
statistics on genetic data to estimate unknown or uncertain parameters. Effective population
Table 3. Principles of how genetic data can be used to obtain estimates of some variables, given that
we from other sources of information know the value(s) of at least some other variables. The
variables considered here are spatial genetic pattern at initiation of the populations (Init), effective
size of each (sub-)population (N), migration rate (m) and the number of generations since LLE
populations were established (age). By "correlation", we mean both autocorrelation within loci and
cross-correlation between loci. For further explanation, see text.
Known variables
Init
N
m
X
X
age
From correlation: find whether initiated as a gradient or not;
then, find age from autocorrelation. If age < 10 gen.: find
initial conditions from FST. If age > 10 gen.: find age from FST
as a double-check.
X
22
Interpretation of statistics
From correlation: find whether initiated as a gradient or not.
If not initiated as a gradient, or age > 20 gen.: find m from
autocorrelation; then, find N from FST (if age > 10 gen.). If
initiated as a gradient: find N from correlation; then, find m
from FST and/or autocorrelation.
Genetic structure in linear habitats
size, effective migration rates, and the length of time since populations were established, are
obviously very important parameters that would be useful to know for a large number of
purposes.
Of course, interpretation of the statistics is not as straightforward in the real world as
in a simulation study. In a case study, we are likely to run into some of the following
obstacles: The populations along the transect are not equally large and not equally spaced,
and therefore the opposing forces of genetic drift and gene flow varies along the habitat. The
"ecological" distances between populations may be hard to determine because we do not know
how different habitat types and barriers influence migration. Population sizes and migration
rates may vary substantially in time. Migration is seldom of the strict stepping-stone type.
Colonization is often not a single event, and the immigration routes may be complex and give
rise to more complex patterns of SGV. Even relatively weak selection (e.g., stabilising
selection) may influence the results strongly. And of course, in a single case study, deviations
from the expected mean of a statistic may be large.
Nevertheless, genetic data offers two aspects of knowledge that we usually cannot
obtain using ecological studies alone. The first is a long-term perspective on population sizes
and migration rates. Ecological studies typically last only a few years, while genetic patterns
may reflect the balance between drift and gene flow for several decades. (The latter is not
always an advantage; when the landscape has changed recently, the current state of affairs
may be much more interesting than estimating parameters that have been averaged over a long
time.) The second is a source of information about patterns and processes in the past. The
simulations presented here shows that some past genetic patterns, such as gradients in allele
frequencies, leave "fingerprints" that last for a long time, while other patterns are not so
simple to detect from the relatively simple statistics we have used here.
There are, however, more sophisticated genetic techniques that can give more
detailed and reliable information on population history. Especially useful is information on
genealogical relationships based on nucleotide-level data on the rapidly evolving mDNA, e.g.
Aars et al. (1998), Clark et al. (1999) and Turner et al. (2000). With such data one can
potentially deduce, e.g., immigration routes (Clark et al.1999). Although an increasing
number of studies employs such techniques, however, they remain relatively time-consuming,
expensive and in demand of good facilities compared to allozymic data. This is especially
relevant with regard to ’third world’ nations, who lags far behind the West regarding
knowledge of nature, especially landscape ecology and the impact of human development on
23
Paper VI
nature. It is therefore important to be able to make the best possible use of simple genetic data
such as allozyme data.
The case study illustrates both the potential of this method and the problems of
interpretation. The relatively strong correlation between ME allozyme frequency (p) and
average wing melanism (AWM) is a quite certain clue that p and AWM varied geographically
in the maternal population before the road verge populations were founded, so that part of the
genetic variance observed today is "ancient" variance. The quite clear cross-correlation pattern
support this conclusion. Probably, p and AWM had their maxima in the area around 15-35
km, declining in both directions (Fig. 6) already before the road was constructed. The
alternative hypothesis, that this pattern of variation has developed after the roadside
populations were established, is unfortunately not easily tested, since many of the source
populations are extinct. It is easier to "test" the age of the roadside populations, which
according to the simulations should be indicated by the observed magnitude of the p-AWM
correlation. Comparing the observed correlation with the simulation results indicates a quite
short time since populations were established, probably not more than 10 years. This fits well
with the fact that much of the road, especially the parts around 15-45 km, was constructed
around 15 years ago, which corresponds to 7-8 wart-biter generations (it has a two-year life
cycle).
The high correlation coefficient, the high spatial autocorrelation and the quite low
FST value indicate that the average population size is closer to 60 individuals than to 15, and
the frequency of migration is likely to be above 0.05 than below.
We have no good
independent measures of neither independent measures of neither migration rate nor
population sizes.
Nevertheless, we have some data that we can use to "guesstimate"
population sizes.
We observed >10 singing males per survey in only four of the 21
populations; the median was 5 singing males per survey. We collected (for analysis) >10
individuals in 14 populations and >20 in six populations. However, we did not collect very
intensively in many of the populations. A better indication comes from the highest ratios
between the number of collected animals and the number of singing males in populations.
This ratio was around 4-6 or more in seven populations (10-15 in two populations!). Thus, to
arrive at a total number of individuals, we can multiply the number of singing males with at
least 4-6. From this we conclude that the median number of individuals per population was at
least 20-30, perhaps as much as 50-70. The prediction that the average population size is in
the order of 60 therefore seems quite plausible.
24
Genetic structure in linear habitats
In the case of the migration rates, Hjermann & Ims (1996) estimated the average
dispersal distance in corn fields to be ca. 40 m. Comparing this distance with the distances
between sampling points along the roadside, 5 % immigrants or more sounds too much.
However, it is likely that animals disperse much longer along a roadside than in a corn field.
From the data published in Hjermann & Ims (1996), it can be estimated that at least 10 % and
more probably 25-50 % of the males emigrate from their original habitat patch (Hjermann,
unpublished results). An immigration rate as high as 5% is therefore at least not entirely out
of the question.
There are some other features of the roadside data that does not agree very well with
the simulations. First, Fig. 6 indicates that there are one ore more coinciding "breakpoints" or
discontinuities in p and AWM (between 11.4 and 13.8 km and between 33.4 and 37.4 km).
This is not expected from the Gradient model, and indicates strong isolation between
neighbouring sampling points or colonization from two different sources. The two hypotheses
does not contradict each other, and either hypothesis is supported by the fact that each of the
two pairs of the aforementioned sampling sites are separated by quite long stretches where the
road runs through forest (700 m in both cases; only three neighbouring sampling points were
separated by more than 300 m forest). The latter hypothesis is supported by the distribution
data, which indicate that not all habitat along the road is saturated. Thus, a combination of the
gradient and step models (scenarios 3 and 4) may have been involved in the process of
roadside colonisation: parts of the roadside are invaded by wart-biters spreading along the
roadside (in contrast to invasion form the surrounding landscape), and the process of invasion
is not yet finished.
The second and perhaps most disturbing anomaly in the roadside data is the
extremely close correspondence between p and AWM in a 37 km long portion of the fragment
(4.8 to 42.5 km, Fig. 6). In the case of the gradient scenario, we would expect p and AWM to
correlate by following roughly the same pattern on a large scale (e.g., increasing to and
thereby decreasing), while they would vary more independently on a finer scale due to genetic
drift. However, p and AWM have strikingly similar ups and downs in this stretch. There are
three possible explanations for this. The first possibility is that the genetic pattern in the
source populations may have been more complicated than a simple gradient or U-shaped
pattern of gene frequencies, perhaps due to patterns of dispersal in this landscape. Secondly,
patterns of dispersal during colonisation of the road may have caused the present pattern, i.e.,
that the colonization routes followed landscape patterns and LLEs rather than straight lines
25
Paper VI
perpendicularly onto the road. Third, p and AWM may be subject to selection pressures that
vary in the same manner geographically, which obviously would invalidate a lot of this
analysis by breaking the assumption of neutral variation.
The latter explanation is not
improbable (e.g., Houle 1989; Karl and Avise 1992; McDonald et al. 1996).
The lack of a significant isolation-by-distance effect on pairwise FST values was at
least partly a result of the large-scale variation in p. Because the large-scale pattern in p is
formed like an inverted U, remote sample points have the same allele frequencies as
proximate sample points, which makes it difficult to determine whether there is an isolationby-distance effect superimposed on this pattern. The data are somewhat ambiguous regarding
genetic differentiation in the one-dimensional roadside versus the two-dimensional,
continuous Alp landscape.
For the ME allele, we found no difference in genetic
differentiation, while colour differentiation between close neighbours was higher in the
roadside, as expected from theory (Kimura and Weiss 1964). The highway is a relatively
recent structure built through farmlands forests, i.e., areas uninhabited by wart-biters prior to
road construction, while the French sample is collected in an ancient habitat where allele
frequencies probably are much closer to an equilibrium between gene flow and genetic drift.
Thus, the genetic pattern in the two landscapes has developed over very different timescales,
which makes it difficult to draw any interferences about differences or similarities in
migration rate. E.g., many of the animals from the intensively sampled road stretch may stem
from a common population, and there may not have been enough time to develop genetic
differences. Also, it is difficult to separate the effect of landscape configuration on dispersal
from the effects of the social setting during dispersal, i.e., dispersal through and to empty sites
along the road vs. dispersal through a landscape saturated with conspecifics.
A somewhat unusual feature of our case study is the use of a phenotypic trait in
place of gene frequencies. It was previously widely believed that polygenic or quantitative
traits would exhibit little or no spatial autocorrelation because the separate distributions for
different loci (unless they are linked) should be essentially independent (Sokal and
Wartenberg, 1983; Epperson 1990, 1993). However, Lande (1991) showed that quantitative
traits can have spatial correlations similar to those for single loci, a result that was confirmed
by Nagylaki (1994) when he reformulated and generalized Lande’s stepping-stone model.
These studies and recent empirical studies of differentiation (e.g., Long and Singh 1995;
Podolsky and Holtsford 1995) demonstrate that phenotypic traits are not outdated as genetic
markers. Because a population phenotypically can be characterised with mean and variance of
26
Genetic structure in linear habitats
the trait, as opposed to frequencies of genes, phenotypic characters may often be a statistically
more powerful tool for differentiating between populations than genetic data. However, the
value of phenotypic traits is much increased if approximate heritability are available; e.g., this
allows estimation of measures of population subdivision such as FST (Kremer et al. 1997).
One of the weak points in our case study is lack of knowledge of the heritability of
melanism in the wart-biter. With the basis in our own observations, we use the following
argument to justify that melanism appears to be mainly genetically controlled, independently
of ME genotype. The alternative hypotheses are that (1) melanism is mainly environmentally
controlled, or (2) it is genetically controlled, but not independently of ME genotype (i.e., the
gene coding for ME may influence melanism through physiological mechanisms, or the ME
and melanism genes may be linked). In Methods, we found that melanism and ME appears to
be completely independent within populations, which refutes (2). We find (1) to be very
improbable, since AWM and p correlates strongly between populations; nothing indicates that
this variation follows any environmental gradient, and nothing indicates that the types of ME
allozymes are environmentally controlled.
Given the abundance of linear habitats and that fairly much theoretical work on
genetic variation in linear population arrays, it is surprising how difficult it is to find empirical
studies of this. One of the few examples is Aars et al. (1998), who studied variation in
mitochondrial DNA among bank voles along a riparian habitat. They found that the genetic
similarity between individuals decreased with distances up to 2 km and flattened out
thereafter.
In contrast, Stacy et al. (1997), who used the same nucleotide sequence and
species in non-linear habitat in the same region, had to increase distance to 30 km to achieve
as low genetic similarity between trapping sites as found by Aars et al. (1998). In addition to
the theoretical effects of linear versus non-linear systems on genetic diversity, Aars and
colleagues hypothesised that long-distance dispersal may be more inhibited in a linear habitat
because resident females may be more successful at defending their territories when the
habitat is only 10 m wide. Furthermore, the large temporal fluctuations in the density of bank
voles in this study area may influence genetic patterns. Thus, genetic theory, behaviour and
population dynamics may all influence population genetic processes, which hints at how
difficult it may be to predict genetic patterns in nature.
We do not claim that the simulation exercise we have presented here in are the
ultimate answer to how linear habitats shape genetic diversity. On the contrary, we realise
that our models only are represent a small part of "model space". E.g., dispersal might extend
27
Paper VI
further than to the nearest neighbour, and the effect of dispersal on gene frequencies is likely
be stochastic rather than deterministic. If animals are distributed continuously along the
habitat, an entirely different class of models should be employed. Incorporating and analysing
the effect of variable population sizes and between-population distances would also make
models much more useful in practice. Lastly, repeated cross-pollination between theory and
empiry has proved to be an effective way to improve biological knowledge. The paucity of
empirical studies on genetic variation in linear versus two-dimensional habitats currently
impedes the advancement of our understanding of this important class of habitats.
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33
Paper VI
Tables
Table 1. Some basic data from the survey of wart-biter (Decticus verrucivorus, D.v.) and its habitat
Norwegian highway, including tests of differences between the east and west side of the road. Tests
were either Pearson goodness-of-fit tests of independence (those reporting χ2) or Mann-Whitney U
tests (those reporting Z, which refers to the standard normal distribution uinder the null hypothesis).
West
East
Total
548
548
1096
classified as habitat
377
360
737
% classified as habitat
69
66
67
83.7
93.5
177.2
in habitat segments
66.3
84.5
150.8
Segments with D.v. (total)
110
149
259
χ2df=1 = 7.69 **
Average presence of D.v. §
0.112
0.125
0.119
Z = -2.09 *
habitat segments only
0.128
0.171
0.149
Z = -3.26 ***
non-habitat segments only
0.076
0.037
0.056
Z = -1.50
% non-habitat of D.v. segments
21
12
17
χ2df=1 = 3.03 (*)
0.153
0.171
0.162
Z = -2.20 *
in all habitat segments
0.176
0.235
0.205
Z = -3.39 ***
in all non-habitat segments
0.101
0.048
0.075
Z = -1.48
in habitat segments with D.v. †
0.771
0.645
0.695
Z = -2.96 **
in non-habitat segments with D.v. † 0.722
0.500
0.627
Z = -2.46 *
Number of 100 m segments
Number of D.v. observed per survey
No. of D.v. per segment per survey
( )
Tests
χ2df=1 = 1.19
* P < 0.10, * P < 0.05, ** P < 0.01, *** P < 0.001
The numbers show the probability of observing D.v. in a segment on a given survey
†
With D.v. on one or more surveys
§
34
Genetic structure in linear habitats
Table 2. Gene frequencies (p) and average wing melanism (AWM) for each sampling location along
the highway. Km denotes distance from the start of the road survey (the two "negative" sampling
points were located outside the surveys strecth) and N denotes the sample size. The last four columns
relate to differences between pairs of successive sampling locations: distance between locations, FST,
the absolute difference in AWM (∆ AWM) and a P-value that summarizes the significance tests of FST
and ∆ AWM.
Relative to next sampling point along road
Km
N
p
AWM
Km
FST §
-45
5
0.20
2.60
30
0,169
-15
29
0.57
2.72
19.8
4.8
4
0.25
2.25
5.9
7
0.71
7.4
21
11.4
'
*
AWM †
Summarized P #
0.12
0,72
0,099
0.47
0,26
1.1
0,235
0.18
0,74
2.43
1.5
-0,020
0.43
0,77
0.60
2.00
4
-0,028
0.40
1,2
10
0.55
1.60
2.4
0,088
2.07
** 0,13
13.8
3
0.83
3.67
3.4
-0,067
1.17
1,26
17.2
16
0.72
2.50
6.1
-0,019
1.14
** 0,58
23.3
12
0.79
3.64
10.1
-0,039
0.03
3,79
33.4
9
0.78
3.67
4
0,076
1.01
37.4
24
0.54
2.65
0.3
0,012
0.53
37.7
29
0.67
3.18
0.8
-0,016
0.55
38.5
20
0.60
2.63
1.3
-0,017
0.49
0,54
39.8
24
0.67
3.13
0.4
-0,034
0.21
1,81
40.2
11
0.73
3.33
0.7
-0,063
0.71
1,29
40.9
8
0.69
2.63
0.3
0,036
0.52
0,26
41.2
14
0.86
3.14
0.3
0,165
0.43
0,09
41.5
16
0.56
2.71
1.3
-0,026
0.10
2,53
42.8
13
0.62
2.62
2.1
0,117
0.62
0,03
44.9
11
0.32
3.23
3.2
-0,011
0.66
0,24
48.1
7
0.50
2.57
0.6
0,033
0.10
1,08
48.7
25
0.70
2.67
6
0,035
0.13
0,52
54.7
39
0.54
2.54
-
-
-
-
*
*
0,014
*
0,09
*
0,32
*
* P < 0.05, ** P < 0.01, *** P < 0.001
§
The indications of statistical significance are results of Fisher exact tests on allele frequencies
† The indications of statistical significance are results of t-tests
#
Summarized P = [P(FST) + P(∆ AWM)]2
35
Paper VI
Table 3. Principles of how genetic data can be used to obtain estimates of some variables, given that
we from other sources of information know the value(s) of at least some other variables. The
variables considered here are spatial genetic pattern at initiation of the populations (Init), effective
size of each (sub-)population (N), migration rate (m) and the number of generations since LLE
populations were established (age). By "correlation", we mean both autocorrelation within loci and
cross-correlation between loci. For further explanation, see text.
Known variables
Init
N
m
X
X
age
From correlation: find whether initiated as a gradient or not;
then, find age from autocorrelation. If age < 10 gen.: find
initial conditions from FST. If age > 10 gen.: find age from FST
as a double-check.
X
36
Interpretation of statistics
From correlation: find whether initiated as a gradient or not.
If not initiated as a gradient, or age > 20 gen.: find m from
autocorrelation; then, find N from FST (if age > 10 gen.). If
initiated as a gradient: find N from correlation; then, find m
from FST and/or autocorrelation.
Genetic structure in linear habitats
Figure legends
Fig. 1. Four scenarios of establishment of LLEs and LLE populations. See text for explanation.
Fig. 2. Outline of the different patterns of spatial genetic variation (SPV) at LLE establishment in the
simulation study. The horizontal axis represent space along the LLE, while the vertical axes
represents pA and pB (the allele frequencies of A1 and B1) for each of the twenty populations along
the LLE. The lines show initial SPV patterns for each of the scenarios Constant, Gradient, Random
and Step (see text for further explanation). In the case of Random, pA and pB is shown with separate
lines. In the case of the three other scenarios, pA = pB and each line thus represent both allele
frequencies.
Fig. 3. Results of the simulation study. The figures show three different measures of genetic
structure (from left to right: FST, spatial autocorrelation, and correlation between loci) at different
times after populations are established in the LLE (from top to bottom: 5, 10, 20 and 50 generations
after establishment). Within each figure, each line represent one combination of scenario and
population size. The secenarios are Constant (open circles), Gradient (filled circles), Random (open
triangles) and Step (filled triangles); population size is N = 15 (unbroken lines) or 60 (broken lines).
On the horizontal axis is the migration rate (the proportion of immigrants from neighbouring
populations). FST measures overall genetic differenatiaton between populations. The spatial
autocorrelation is the correlation (Spearmans rank correlation coefficient) in allele frequencies
between neighbouring populations (lag = 1; averaged for the two loci). The correlation between loci
is correlation in allele frequencies between the two loci, measuerd by Spearmans rank correlation
coefficient. See text for more details.
Fig. 4. Outline of sampling areas of this study. The roadside habitat was not completely straight in
reality. In the case of the roadside, the thin inner lines above and below the km-line represent habitat
on the east and west side of the road, respectively, and the thick outer lines show where male wartbiters were observed. The crosses above the lines show where we sampled animals for analysis
(without regard to which side of the road we sampled).
Fig. 5. Autocorrelation of wart-biter abundance. (a) for each roadside. (b) Cross-correlation between
roadsides for different spatail lags (c) Abundance in 5 km segments corrected for autocorrelation
Fig. 6. Allele frequencies (p) of allele 1 of the ME enzyme and average wing melanism (AWM)
along the Norwegian transect (a), the Norwegian subtransect in detail (b) and along the French
transect (c).
37
Paper VI
Fig. 7. (a) Autocorrelation for allele frequency (p) and melanism (AWM) and in the Norwegian
transect. (b) Cross-correlation between allele frequency (p) and melanism (AWM). In both panels,
"lag" (on the horizontal axis) is number of populations, and Spearman’s correla
38
Genetic structure in linear habitats
1
(a)
5
p
AW M
0,8
4
p
3
0,4
AWM
0,6
2
0,2
0
1
-50
-40
-30
-20
-10
0
10
20
30
40
50
60
Dista nce a long tra nse ct (km )
1
(c) 1
5
0 ,8
5
0,8
4
4
0 ,6
0 ,4
3
p
p
3
AW M
0,6
AW M
(b)
0,4
2
0 ,2
2
0,2
p
p
AWM
0
AWM
1
37
38
39
40
41
42
Dis ta nc e along tra ns ec t (k m )
0
1
0 1 2 3 4 5 6 7 8 9
Dis ta nc e along tra ns ec t (k m )
Figure 8. Allele frequencies (p) of allele 1 of the ME enzyme and average wing melanism (AWM)
along the Norwegian transect (a), the Norwegian subtransect in detail (b) and along the French
transect (c).
tion coefficient was used. The eight populations in the Norwegian subtransect were pooled to two
populations (see Methods). Correlation values above/below broken lines are statistically significant
(P<0.05).
39
Paper VI
(a)
(b)
1
0,4
W es t, s im ple autocorrelation
W es t, partial autocorrelation
East, sim ple autocorrelation
East, partial autoc orrelation
0,6
0,4
0,2
0
0
1
0,3
Corre lation coe fficie nt
C orre lation coe fficie nt
0,8
2
0,2
0,1
3
Lag (km)
-0,2
0
-3
-2
-1
0
1
2
Lag (km)
(c)
2
Re lativ e abundance
1,5
1
0,5
East
W es t
0
-0,5
-1
-1,5
0
10
20
30
40
50
D istance along transe ct (km)
Figure 9. Autocorrelation of wart-biter abundance. (a) for each roadside. (b) Cross-correlation
between roadsides for different spatial lags (c) Abundance in 5 km segments corrected for
autocorrelation.
40
3
Genetic structure in linear habitats
Table 1. Some basic data from the survey of wart-biter (Decticus verrucivorus, D.v.) and its habitat
Norwegian highway, including tests of differences between the east and west side of the road. Tests
were either Pearson goodness-of-fit tests of independence (those reporting χ2) or Mann-Whitney U
tests (those reporting Z, which refers to the standard normal distribution uinder the null hypothesis).
West
East
Total
548
548
1096
classified as habitat
377
360
737
% classified as habitat
69
66
67
83.7
93.5
177.2
in habitat segments
66.3
84.5
150.8
Segments with D.v. (total)
110
149
259
χ2df=1 = 7.69 **
Average presence of D.v. §
0.112
0.125
0.119
Z = -2.09 *
habitat segments only
0.128
0.171
0.149
Z = -3.26 ***
non-habitat segments only
0.076
0.037
0.056
Z = -1.50
% non-habitat of D.v. segments
21
12
17
χ2df=1 = 3.03 (*)
0.153
0.171
0.162
Z = -2.20 *
in all habitat segments
0.176
0.235
0.205
Z = -3.39 ***
in all non-habitat segments
0.101
0.048
0.075
Z = -1.48
in habitat segments with D.v. †
0.771
0.645
0.695
Z = -2.96 **
in non-habitat segments with D.v. † 0.722
0.500
0.627
Z = -2.46 *
Number of 100 m segments
Number of D.v. observed per survey
No. of D.v. per segment per survey
Tests
χ2df=1 = 1.19
( )
* P < 0.10, * P < 0.05, ** P < 0.01, *** P < 0.001
The numbers show the probability of observing D.v. in a segment on a given survey
†
With D.v. on one or more surveys
§
41