Spatial ecological and genetic structure of a mixed population of sexual diploid and apomictic triploid dandelions

Authors


 P. G. Meirmans, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Kruislaan 318, 1098 SM, Amsterdam, the Netherlands. Tel.: +31 205 257 856; fax: +31 205 257 662; e-mail: meirmans@bio.uva.nl

Abstract

Abstract Ecological differentiation is widely seen as an important factor enabling the stable coexistence of closely related plants of different ploidy levels. We studied ecological and genetic differentiation between co-occurring sexual diploid and apomictic triploid Taraxacum section Ruderalia by analysing spatial patterns both in the distribution of cytotypes and in the distribution of genetic variation within and between the cytotypes. A significant relationship between ploidy level and elevation was found. This mode of ecological differentiation however, was not sufficient to explain the significant spatial structure in the distribution of diploids and triploids within the population. Strong congruence was found between the spatial genetic patterns within the diploids and within the triploids. We argue that this congruence is an indication of gene flow between neighbouring plants of different ploidy levels.

Introduction

Although polyploidy is one of the major aspects of plant evolution, the mechanisms by which newly formed polyploids can become established in their parent populations remain unclear. Central to polyploid theory is Levin's (1975) minority cytotype exclusion principle that predicts which two conspecific cytotypes cannot coexist stably. Fitness loss caused by unsuccessful hybridization will occur more frequently in the less than in the more abundant cytotype, and this will ultimately lead to the exclusion of the least abundant cytotype from the population. Newly formed polyploids will often start as a minority cytotype in an existing population, so their establishment seems very unlikely, except in small populations where drift is an important factor. Coexistence of two cytotypes can be possible however, when there is increased self-compatibility in the minority cytotype or when there is ecological differentiation between the cytotypes (Fowler & Levin, 1984; Rodriguez, 1996; Felber & Bever, 1997).

In almost all asexually reproducing plant species, asexuality is linked with polyploidy (Stebbins, 1980). In polyploid complexes comprising both asexual polyploid and sexual diploid individuals, the cytotype exclusion principle works differently and will always lead to the exclusion of diploids from mixed populations of any composition. Assuming that the asexual polyploids still produce pollen but do not need pollination to produce seeds, unsuccessful hybridizations will only take place in the sexual diploids, which leads to a selective disadvantage of the diploids. Furthermore, diploids can produce polyploid offspring from pollinations from polyploid fathers, but the polyploids will always produce only polyploid offspring. This will cause a decrease in the relative frequency of diploids in the population and will thus lead to more frequent hybridizations, which in turn will decrease the relative frequency of diploids even further (Mogie & Ford, 1988).

Ecological differentiation has been proven for several polyploid complexes, including some complexes with asexually reproducing polyploids (see Petit et al., 1999 for an overview). Most of these studies have focused on ecological differences among diploid, mixed and polyploid populations, but only few have studied within-population differentiation. As most ecological variables are spatially structured (Legendre & Legendre, 1998), ecological differentiation between cytotypes leads to the expectation of patchy distribution of the cytotypes within a population. Only few studies have investigated spatial patterns within populations of coexisting cytotypes (Keeler, 1992; Meirmans et al., 1999; Husband & Schemske, 2000; Hardy & Vekemans, 2001). Husband & Schemske (2000) and Hardy & Vekemans (2001) found significant patterns in their species, respectively, Chamerion angustifolium and Centaurea jacea. Both Keeler et al. (1987) and Meirmans et al. (1999) found no spatial structure in the distribution of cytotypes of Andropogon gerardii and Taraxacum sect. Ruderalia, respectively.

The polyploid complex Taraxacum section Ruderalia Kirschner, H. Øllg. & Štěpánek (dandelions, Asteraceae) contains both diploid (2n=2x=16) and triploid (2n=3x=24) individuals, whereas higher ploidy levels are rare. Diploid Ruderalia reproduce obligatorily sexually and are usually self-incompatible whereas triploid Ruderalia reproduce through apomixis but nevertheless produce pollen that is largely sterile. Based on the cytotype exclusion mechanisms and the fact that diploids and triploids are frequently found together (Den Nijs & Sterk, 1980), ecological differentiation is expected in Taraxacum sect. Ruderalia. Tschermak-Woess (1949) and Fürnkranz (1966) found a difference in flowering time between the ploidy levels: in Central Europe, diploids flower approximately 1 week earlier than co-occurring triploids. The significance of this difference can, however, be questioned as there still is a lot of overlap between the respective flowering periods. Elzinga et al. (1987) report a preference of diploids for relatively warm south facing slopes in the southern part of the Netherlands. Meirmans et al. (1999) found that the relative frequency of triploids in populations from Neuchâtel, Switzerland, increased with an increase in the amount of disturbance by human activities.

Apomixis, as well as some forms of ecological differentiation (e.g. in flowering time), will lead to reproductive isolation between two cytotypes. Such reproductive isolation has been found in several polyploid complexes (Petit et al., 1997; Van Dijk & Bakx-Schotman, 1997; Gauthier et al., 1998a), but genetic studies show that in Taraxacum section Ruderalia this is not the case. Menken et al. (1995) found large homogeneity in allozyme allele frequencies between diploids and triploids from mixed populations. This intrapopulational homogeneity between ploidy levels contrasted strongly with the genetic differentiation between different populations. As this analysis was performed by analysing population level variation, the spatial scales at which the interactions between diploids and triploids take place within a population remain unknown.

As a result of limited seed dispersal and spatially restricted pollination, genetic variation may not be distributed homogeneously over a population (isolation by distance; Wright, 1943). If this holds true for Taraxacum, the asexuality of the triploids leads to clear expectations regarding the genetical population structure. If the triploids are strictly asexual and reproductively isolated from the diploids, the spatial genetic patterns of the two cytotypes should be independent. The two spatial genetic patterns are expected to differ as isolation by distance in the diploids builds up as a result of both restricted seed and pollen dispersal whereas in the triploid it depends on the seed dispersal only. If there is some gene flow between the two cytotypes, the two spatial genetic patterns should show congruency, although they might still be slightly different.

The aim of this study is to look for ecological and genetic differentiation within a mixed diploid–triploid population of Taraxacum sect. Ruderalia. Ecological differentiation between cytotypes is studied by analysing the spatial distribution of cytotypes within the population and its relation to the elevation pattern within the field. Genetic differentiation within and between the ploidy levels was studied by analysing the spatial distribution of allozyme variation and comparing the spatial patterns found in diploids and triploids.

Materials and methods

Sampling

In spring 1986, we studied a Taraxacum sect. Ruderalia population from Waldmichelbach/Oberschönmattenwag in Odenwald, Germany. This is the same locality, but not the same sample, as population number T20 from Menken et al. (1995). The population was situated in a moderately manured haymeadow, c. 30 m wide and 110 m long. At the time of sampling, the field had been in use as a haymeadow for c. 25 years. In the middle of the field, a grid was laid out measuring 25 × 90 m, subdivided in 360 subplots of 2.5 × 2.5 m. For every subplot, the ratio of diploid and triploid Taraxacum individuals was estimated by analysing 10–15 plants using the pollen-analysis method of Tschermak-Woess (1949). Due to disturbed meiosis, pollen from triploids is irregularly sized, whereas pollen from diploids is regularly sized; simply checking the pollen under a field microscope is a quick method for determining the ploidy level of an individual. The accuracy of the method has been verified with chromosome counts (Den Nijs & Sterk, 1980). The elevation of each subplot was measured in spring 2000, using a level instrument. As the corners of the grid were marked when leaving the field in 1986, it was possible to exactly reconstruct the grid in 2000.

Based on the overall cytotype distribution, four subpopulations (A, B, C and D, see Fig. 1), each comprising several adjacent subplots, were chosen for further analysis. From these subpopulations, a total of 421 plants were randomly picked out, checked for ploidy level, mapped, dug out and transported to the greenhouse in Amsterdam.

Figure 1.

Odenwald study field and the gridsystem of the analysis. Thin lines indicate borders of subplots. Bold lines indicate borders of subpopulations used for genetic analysis.

Electrophoresis

We performed allozyme analysis on 361 (86%) plants that survived the transfer to Amsterdam. No distinct pattern was detectable in the distribution of the died plants within the field, so we assume that any selection during the transport of the plants has had no influence on our analysis. Protein extraction, electrophoresis and allozyme specifications followed the protocol of Menken et al. (1989). Two enzyme systems were used: 6-phosphogluconate dehydrogenase (with two loci: 6Pgdh-1 and 6Pgdh-2) and malate dehydrogenase (with one locus: Mdh-1). All three enzymes are dimeric and in the absence of dosage compensation allow for easy recognition of both kinds of triploid heterozygotes, the loci are located in the nuclear DNA, show Mendelian inheritance, and are unlinked (Menken et al., 1989).

Genetic population structure

Allozyme data from the four subpopulations was analysed for deviation from Hardy–Weinberg (HW) expectations for both diploids and triploids, using the log likelihood G-statistic. For triploids HW-expectations were calculated following (p + q)3 for a locus with two alleles (Menken et al., 1995), significance was assessed by permutating alleles between individuals. Fis values (Nei, 1987) were calculated for both ploidy levels. The calculated Fis values were not used as test statistics for testing HW equilibrium, as in triploids a population with Fis=0 may be out of equilibrium. Imagine, for example, a population consisting for 25% of genotype aaa and 75% of genotype AAa. This population would have a Fis of zero as the frequency of heterozygotes exactly matches the expectation of 1–2p3 (=0.75). The population is nevertheless clearly out of HW equilibrium as it lacks two of the four possible genotypes.

Differentiation in allele frequencies between pairs of subpopulations was tested using the G-statistic, for diploids and triploids separately. Significance was determined by randomising genotypes between pairs of populations. This permutation scheme was chosen as it does not assume random mating within the subpopulations (Goudet et al., 1996). The same method was used to test for differentiation between diploids and triploids from the same subpopulation. When necessary, significance levels were corrected for multiple testing using the sequential Bonferroni procedure (Rice, 1989).

Spatial analysis

Spatial autocorrelation analysis tests the association of the value of a geographically distributed variable (here, cytotype and allele frequencies) with the value of the same variable at another location (Sokal & Oden, 1978). Geographical relationships between pairs of samples are grouped into a number of distance classes and for every distance class an autocorrelation coefficient is calculated. As autocorrelation analysis involves multiple testing, correction is necessary. Therefore, Hewitt et al. (1997) developed the progressive Bonferroni correction, a correction method that is especially meant for correlograms.

For analysing spatial patterns in the distribution of the cytotype ratio over the 360 subplots, we used Moran's I (Moran, 1950), with 35 distance classes, where the input variable was the fraction of diploids found in the subplots (the fact that the number of distance classes equals the number of columns on our sampling grid is entirely coincidental). For the analysis of correspondence between spatial patterns in cytotype distribution and elevation, we used a combination of standard Mantel tests (Mantel, 1967) and partial Mantel tests (Smouse et al., 1986). Standard correlation analysis methods are not appropriate in cases where both variables are spatially autocorrelated (Legendre, 1993). This is the case here, where both the cytotype ratio and the elevation of the subplots are spatially dependent. A method to test the relationship between two spatially dependent variables is to perform a partial Mantel test that calculates the relationship between two variables while correcting for the influence of a third one. We used a series of four Mantel and partial Mantel tests to elucidate the relationships between ploidy, elevation and space (see Table 1).

Table 1.  (Partial) Mantel tests for association between spatial distance, elevation, and difference in percentage of diploids for the 360 subplots.
Matrix AMatrix BCorrected for:Mantel's r
  • **

    P  < 0.001 after Bonferroni correction.

Geographical  distancePercentage  of diploids0.185**
Geographical  distancePercentage  of diploidsElevation0.172**
ElevationPercentage  of diploids0.123**
ElevationPercentage  of diploidsGeographical distance0.102**

Analysis of fine-scaled patterns in the distribution of allelic variation was possible as the spatial co-ordinates of every sampled plant were measured in the field. For this analysis we used the coefficient of relationship, ρij, which is independent of ploidy level, following Hardy & Vekemans (2001). Under two-dimensional isolation by distance, the coefficient of relationship between individuals is expected to linearly decrease with the logarithm of the distance between the individuals. The coefficient of relationship between two individuals is defined as ρij=σij/σ2, where σij is the covariance between the allele frequency of individuals i and j, and σ2 is the variance of the allele frequency in the cytotype. A multilocus, multiallele estimation can be calculated by weighing the contributions of individual alleles by pla(1 − pla), where pla is the frequency of the ath allele at the lth locus (Loiselle et al., 1995). The coefficient of relationship can also be used to calculate relationships between individuals of different ploidy levels. In that case it is defined as: ρij=σij/σd·σt, where σd and σt are the standard deviations of the allele frequencies for the diploids and triploids, respectively, and σij is calculated using the cytotype specific allele frequencies.

Spatial autocorrelation analysis was performed by calculating ρij for every pair of individuals. The matrix of pairwise geographical distances was divided into 10 distance classes, and for every distance class the average ρij was calculated. The upper limits of the 10 distance classes were 0.25, 0.5, 1, 2, 4, 8, 16, 32, 64 and 128 m. Significance was assessed by randomizing genotypes over the distance classes. This test was performed for the diploids and the triploids separately and for the interaction between diploids and triploids.

The number of randomizations for all permutation tests mentioned above was 9999. Calculations for the patterns in the distribution of the cytotypes were performed using the software package ‘r’, version 4.0d3 (Legendre & Vaudor, 1991). Genetic autocorrelation analyses were performed using the program AutocorG (available upon request from ohardy@ulb.ac.be). The G-tests were performed by a Perl script run in macperl 5.2.

Results

Distribution of cytotypes

The pollen analysis for the distribution of the cytotypes over the entire field showed that diploids were the minority cytotype: 33.6% of the analysed plants were diploid, the remaining 66.4% were triploid. In 37 of the 360 subplots no diploids were found; the maximum percentage of diploids in a single subplot was 90%. The cytotypes were not randomly distributed over the field; two areas could be discerned in which the percentage of diploids was higher than elsewhere (Fig. 2). The correlogram (Fig. 3) shows the significance of this heterogeneous distribution; the majority of the distance classes shows a significant spatial autocorrelation. For distances smaller than 21 m there is a significant positive autocorrelation, meaning that subplots less than 21 m apart are more equal in cytotype ratio than would be expected from random distribution. For distances larger than 57 m there is a significant negative autocorrelation, meaning that subplots more than 57 m apart are less equal in cytotype ratio than would be expected from random distribution.

Figure 2.

Distribution of cytotypes over the sample field. The greyscale indicates the percentage of diploids found in a subplot after analysis of 10–15 individuals.

Figure 3.

Correlogram for spatial patterns of variation of the percentage of diploids in the 360 subplots. Black symbols indicate significance ( P  < 0.05) after progressive Bonferroni correction.

There appears to be an association between the cytotype ratio of the subplots and the topography (relief) of the field (Fig. 2). This relationship was tested using a series of (partial) Mantel tests (Table 1). The first standard Mantel test showed, like the correlogram, a significant (P < 0.001) positive relationship between the geographical distance and the difference in cytotype ratio. The second partial Mantel test tested the same relationship, corrected for the influence of the elevation. This test showed only a slight decrease in the value of rM compared with the uncorrected test; the corrected relationship between space and cytotype ratio remained significant at the P < 0.001 level. Elevation per se therefore explains only a small part of the spatially dependent variation in the cytotype ratio. The third test tested directly for the relationship between elevation and cytotype ratio, and showed a strong relationship between these two variables. The last test tested what part of this relationship was caused by autocorrelation present in both variables, by correcting for geographical distance. Compared with the uncorrected test, there was only a slight difference in rm, and the test was still strongly significant (P < 0.001). This indicates that spatial autocorrelation in the data explained only a small part of the observed correlation between cytotype ratio and elevation.

Genetic analysis

A total of 11 alleles were found, four for 6Pgdh-1, three for 6Pgdh-2 and four for Mdh-1. Most alleles were shared by the two cytotypes; out of 11 alleles, three were cytotype specific, but these had an overall frequency lower than 2% (see Table 2).

Table 2.  Allele frequencies for both ploidy levels, for each subpopulation separately and for all subpopulations combined.
  Allele
  6Pgdh-16Pgdh-2Mdh-1 
PloidySubpopabcdabcabcdn
  1. Numbers in bold indicate frequencies of cytotype specific alleles per subpopulation.

2xA0.230.770.000.000.020.100.880.000.000.230.7747
3xA0.070.850.080.010.000.090.910.010.000.190.8157
2xB0.000.780.220.000.000.220.780.000.000.360.6437
3xB0.010.740.230.030.0030.130.870.030.000.210.76102
2xC0.060.650.290.000.000.290.710.000.020.170.8124
3xC0.070.630.310.000.000.230.780.000.000.180.8340
2xD0.060.700.240.000.000.140.860.000.020.150.8333
3xD0.050.730.220.000.000.370.630.000.000.060.9421
2xall0.100.740.160.000.010.170.820.000.010.240.76141
3xall0.040.750.200.020.0020.160.840.010.000.180.80220

In the triploids, 46 different three-locus genotypes (‘clones’) were found, 23 of these were found only once. The most frequent clone was found 41 times: 29 times in subpopulation B (where it made up 28% of the sampled triploids), seven times in C, five times in A and it was absent from subpopulation D. The next-most frequent clone was found 34 times; 23 times in A (=40% of the sampled triploids), five times in B, four times in C and two times in D. Most other clones that were found more than once were also unevenly distributed over the subpopulations.

Most inbreeding coefficients in both the diploids and the triploids were slightly negative (Table 3). In the diploids, none of the tests revealed significant deviations from Hardy–Weinberg expectations; in the triploids only two of 12 tests showed a significant deviation. In one of these two cases (locus 6Pgdh − 1 in subpopulation C), the Fis value was remarkably close to zero, illustrating the uselessness of Fis as a statistic for testing for random mating in a polyploid population.

Table 3.  Inbreeding coefficients and Hardy–Weinberg equilibrium. Shown are Fis values calculated separately for diploids and triploids. Fis values were not tested for deviation from 0, as in triploids an Fis of 0 does not necessarily imply random mating. Instead, deviation from HW expectations was tested using a G -statistic.
 ABCD 
  • *

    P  < 0.05 after sequential Bonferroni correction.

6Pgdh1−0.15−0.100.18−0.13Diploids
0.16−0.060.02*−0.08Triploids
6Pgdh-2−0.10−0.10−0.19−0.14Diploids
0.06−0.06−0.080.14Triploids
Mdh-10.09−0.25−0.18−0.06Diploids
0.17−0.20*−0.02−0.03Triploids

The pairwise tests for subpopulation differentiation (Table 4) showed significant differentiation between most subpopulations. Only subpopulations C and D were not significantly differentiated, both in the diploids and in the triploids. Allele frequencies in the diploids and triploids from the same subpopulations were significantly different in subpopulations A and B, but not in C and D.

Table 4. P -values from pairwise tests of multilocus subpopulation differentiation. Values above diagonal are from tests between diploids from different subpopulations; values below diagonal are from tests between triploids from different subpopulations. The values on the diagonal (grey) represent tests between diploids and triploids from the same subpopulations.
SubpopABCD 
  • *

    P  < 0.05 after sequential Bonferroni correction.

A0.0003*0.0001*0.0001*0.0001*Triploids
B0.0001*0.0083*0.0002*0.0002* 
C0.0001*0.0035*0.69900.0408 
D0.0001*0.0008*0.51830.0241 
Diploids    

Spatial genetic analysis

The correlograms calculated separately for diploids and triploids show some similarity (Fig. 4a,b) although they do differ in significance at certain distance classes. Both correlograms show positive autocorrelation for distance classes up to 16 m, and negative autocorrelation for distance classes at 32 and 128 m. This means that individuals less than 16 m apart are genetically more similar to each other than would be expected from a random distribution. Individuals which grow more than 16 m apart are genetically less similar to each other than would be expected from a random distribution. For both ploidy levels, the correlograms are globally significant (P < 0.001).

Figure 4.

Coefficient of relationship ριj (dark line) as a function of distance in diploids (a) , in triploids (b) and between diploids and triploids (c). Black symbols indicate significance ( P  < 0.05) after progressive Bonferroni correction.

The similarity in the spatial genetic patterns of the two ploidy levels which is apparent from Fig. 4(a,b) does not necessarily imply that there is genetic exchange between diploids and triploids. In case of independence of the isolation by distance structures, there would be no local genetic relationships between diploids and triploids, but simply equal patch sizes. To test this, a third correlogram was computed, including only distances between diploids and triploids, leaving out diploid–diploid and triploid–triploid comparisons. The structure in this third correlogram (Fig. 4c, global test: P < 0.001) is practically the same as the structure of the correlograms calculated separately for the two ploidy levels. This shows that diploids and triploids growing in each others' direct vicinity are more related to each other than diploids and triploids growing further apart.

Discussion

Distribution of cytotypes

Based on the minority cytotype exclusion principle (Levin, 1975; Fowler & Levin, 1984; Felber & Bever, 1997), ecological differentiation between coexisting cytotypes is expected. This may lead to a patchy distribution of the cytotypes within a population as a result of ecological heterogeneity. Of the studies known to us where within-population cytotype distribution was analysed (Keeler, 1992; Meirmans et al., 1999; Husband & Schemske, 2000), two were able to detect significant spatial structuring. Husband & Schemske (2000) reported that in the population of C. angustifolium they studied, different patches of plants had different ratios of diploids and tetraploids, but they made no further inference on the causes of this patchy distribution. Hardy & Vekemans (2001) used autocorrelation statistics to show spatial segregation of diploid and tetraploid C. jacea, but they did not test for any ecological mechanisms to explain the segregation. Meirmans et al. (1999) found no spatial pattern in the distribution of cytotypes in an analysis of four transects through a single population of Taraxacum sect. Ruderalia in north-west Switzerland. As this population was chosen because of an apparent ecological homogeneity, the absence of spatial patterns in cytotype distribution may not be surprising. The mechanisms enabling the coexistence of the cytotypes in that population, however, remain unknown. In Keeler's (1992) study of A. gerardii, the lack of spatial structure may be the result of a lack of statistical power rather than of the absence of any spatial patterns within the populations. We re-analysed her data using Moran's I statistic (results not shown) and found that significant autocorrelation patterns were present in two of the four populations she presented as being representative. So there probably is some ecological differentiation between the two cytotypes of A. gerardii.

In the present study, the spatial autocorrelation test showed that there is a highly significant patchy distribution of the two Taraxacum cytotypes in the Odenwald population studied. This patchy distribution may explain the difference between the overall cytotype ratio we found (34% diploids) and the ratio Menken et al. (1995) found (60% diploids) as they sampled only from a small part of the field (pers. comm.). The series of (partial) Mantel tests also showed that there is ecological differentiation between diploids and triploids: the correlation between cytotype ratio and elevation was highly significant, and remained so when correcting for the influence of spatial autocorrelation in both variables. This relation between cytotype and elevation nevertheless only explained a small part of the spatial autocorrelation in the distribution of the cytotypes, as is shown by the small decrease of the Mantel correlation coefficient when correcting for elevation. This means that the observed heterogeneity in the distribution of the cytotypes is predominantly caused by factors other than elevation. These may either be ecological variables not measured in our study, or demographic factors. Different parts of the field may have different colonization histories, the results of which may still be visible in the present day distribution of the cytotypes. Another possibility is that the observed distribution is the result of a kind of ecological ‘isolation by distance’ process. As a result of limited seed dispersal, patches of cytotypes may develop, comparable with the patches of alleles or haplotypes that are the result of genetic isolation by distance processes (Sokal et al., 1989).

The Mantel approach does not provide a direct indication of the exact nature of the correlation between cytotype ratio and elevation; it does not tell which ploidy level prefers higher elevations and which prefers lower elevations, but simply states that plots from the same elevation have comparable cytotype ratios. A look at the distribution map (Fig. 2), however, tells that diploids are more frequent at higher elevations, and triploids at the lower.

The precise ecological effect of elevation on the two cytotypes is unclear. Possibly, elevation influences the drainage patterns of the field. Water flowing down from the woods above the field may be flowing predominantly through the little ‘trough’ in the middle causing small-scale differences in moisture and texture of the soil and differences in temperature regime. On a regional scale in Neuchâtel, Switzerland, Meirmans et al. (1999) found a relation between the presence of triploids and the amount of disturbance caused by human activities. Although, according to the owner, the Odenwald field under study here has experienced a low intensity management for at least the last 15 years before our sample, the field has occasionally been grazed by cattle. These can display preferences for certain parts of the field and thus create differences in the amount of disturbance. Besides this, certain parts of the field may be more vulnerable to trampling (e.g. because they are wetter due to the local drainage patterns described above), and ecological differences within the field may increase because of the presence of grazers.

As a result of cytotype exclusion principles (Levin, 1975; Felber & Bever, 1997), a stable coexistence of two ploidy levels is not expected unless there is some form of ecological differentiation between them. It can be questioned however, whether the difference in elevation we found between diploids and triploids provides a strong enough ecological differentiation to promote long-term coexistence, as the elevation explains only a small part of the variation in ploidy level.

Distribution of genetic variation

As a result of hybrid inviability, coexisting cytotypes are expected to show some form of reproductive isolation. Genetic studies have proven that reproductive isolation is present in polyploid complexes with sympatric cytotypes such as Arrhenatherum elatius (Petit et al., 1997) and Plantago media (Van Dijk & Bakx-Schotman, 1997), but absent in others such as the Lotus alpinus/corniculatus complex (Gauthier et al., 1998a,b). In Taraxacum sect. Ruderalia reproductive isolation is expected between the cytotypes because of the apomictic mode of reproduction of the triploids. Nevertheless, Menken et al. (1995) showed that there was high homogeneity in allele frequencies between diploids and triploids from mixed populations. The Odenwald population in this study was one of the populations previously sampled by Menken et al. (1995); they found no significant genetic differentiation between diploids and triploids. In our study, however, we found significant differences in allele frequencies between diploids and triploids in two of the four subpopulations (A and B). This difference between our results and those of Menken et al. (1995) may be a result of the difference in power of the tests, as they sampled a total of 44 plants and tested single-locus, we sampled on average about 90 plants per subpopulation and used a multilocus statistic. Subpopulations C and D, in which we found no differentiation between the two cytotypes, are also the two subpopulations with the smallest sample sizes, which may also indicate that lack of significant differentiation may be due to a lack of statistical power.

Usually, within-population differentiation is ascribed to isolation by distance mechanisms caused by restricted gene flow (Peakall & Beattie, 1995; Hossaert-McKey et al., 1996; Streiff et al., 1998). If isolation by distance mechanisms are indeed the cause of the spatial genetic patterns found in the studied Taraxacum population, the congruence between patterns of the two ploidy levels would imply gene flow between the sexual diploids and the apomictic triploids. Hardy & Vekemans (2001) found no such congruence in the spatial distribution of allozyme variation within mixed populations of diploid and tetraploid C. jacea and concluded that at this spatial scale, the two cytotypes were reproductively isolated.

The most probable mechanism for gene flow between the cytotypes of Taraxacum sect. Ruderalia is hybridization between triploid fathers and diploid mothers (Morita et al., 1990b). Triploids produce seeds by means of apomixis for which no pollen input is required, but they also produce pollen. Male meiosis in triploids is highly disturbed and as a result of this, pollen of irregular ploidy is produced, most of which is aneuploid and sterile. Crossing experiments between triploid fathers and diploid mothers resulted in very low seedset. Calame (2000) found 28.5% seedset in handpollinated crossings and 10.6% seedset in diploid plants which were transplanted into a fully triploid field. Tas & Van Dijk (1999) found a seedset of 22% after manual cross-pollinations. Triploid pollen is known to induce breakdown of the self-incompatibility system of diploids (Morita et al., 1990a), so possibly a large part of the seedset of these crossing experiments is the result of selfing. Tas & Van Dijk (1999) screened the offspring from their crosses for allozyme variation and found that 88% resulted from selfing and in most of the remaining 12% real hybrids seedset was reduced. Despite these results, hybridization may very well occur in the wild. Calame (2000) found that among the offspring of diploid plants transplanted into a triploid field, 8.4% was triploid and 2.2% was tetraploid. The high incidence of tetraploids in experimental hybridizations (sometimes higher than 50%, R. van der Hulst, pers. comm.) contrasts strongly with the low incidence in wild populations (Meirmans et al., 1999). The lack of tetraploids in the field, the breakdown of self-incompatibility and the reduced fertility of the hybrids all make the order of magnitude of the effective hybridization rate in wild populations still unknown, although hybrids are readily obtainable from crosses and transplantation experiments.

There are no theoretical models that relate the amount of congruence in within-population spatial genetic patterns to the level of hybridization between two ploidy levels. The only theoretical study (Hardy & Vekemans, 2001) included hybridization between ploidy levels, modelled isolation by distance between populations rather than within a population and found that the correlation between the isolation by distance patterns of diploids and tetraploids indeed increases with decreasing hybridization barrier. In general, the spatial structure within the diploids was much stronger (higher Fst/(1−Fst)) than within the tetraploids, as a result of the higher effective population size for the tetraploids at an equal number of individuals. This effect was also visible in our study population (Fig. 4). In Hardy and Vekemans' model, the Fst/(1−Fst) value for the smallest distance classes, calculated between ploidy levels, became intermediate between the values for the diploids and the tetraploids at high (10%) levels of hybridization. In our study the correlogram calculated between cytotypes was indeed an intermediate between the two within-cytotype correlograms (Fig. 4). Assuming that the results for the between-populations model of Hardy and Vekemans is also applicable to within-population trends, this might indicate a hybridization rate which is remarkably high considering the results of experimental crossings (Tas & Van Dijk, 1999; Calame, 2000).

Sokal et al. (1989 ) modelled the effects of selection on spatial genetic patterns and tested this using autocorrelation statistics. They found that spatial selection gradients yielded clear clinal correlograms. Other types of spatially restricted selection, such as patches, also resulted in significant autocorrelations, although the correlogram patterns were less clear. Selection therefore could provide an alternative explanation for the spatial genetic patterns we observed in Taraxacum . If the same selection would act on the diploids as well as on the triploids, it would also explain the congruence between the cytotypes. However, the multilocus correlograms we presented are much clearer and more significant than each of the three single-locus correlograms (not shown) which suggests that there is redundancy between spatial patterns present in the loci. This redundancy would suggest that the selection works in tandem on different, unlinked and presumably neutral allozyme loci. We therefore conclude that the observed congruence between the spatial genetic patterns of the two ploidy levels is not the result of selection, but the result of gene flow between the diploid sexuals and the triploid apomicts.

High levels of gene flow between sexual and apomictic Taraxacum would result in the constant creation of new polyploid lineages, and would explain the high number of different triploid genotypes usually found in population samples of Taraxacum (Van der Hulst et al., 2000). Van der Hulst et al. (2000) found a high number of genotypes in samples from three purely triploid populations. They showed that the distribution of AFLP-markers over the genotypes was more compatible with a sexual than with a clonal population structure. The diploid–triploid cycle and the constant creation of new clonal lineages may therefore not only have an influence on the population structure of mixed populations, but also on the structure of purely triploid populations, although these populations may be hundreds of kilometres away from the diploid distribution area.

Acknowledgments

The authors would like to thank Annemieke Kiers, Frans van Dunné, Gerard Oostermeijer and two anonymous reviewers for valuable comments on the manuscript. Olivier Hardy kindly provided the AutocorG program.

Received: 17 April 2002;accepted 19 July 2002

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