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AOBPreview originally published online on September 19, 2007
Annals of Botany 2007 100(6):1259-1270; doi:10.1093/aob/mcm204
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© The Author 2007. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Population Dynamics of Diploid and Hexaploid Populations of a Perennial Herb

Zuzana Münzbergová1,2,*

1 Institute of Botany, Academy of Sciences of the Czech Republic, Zámek 1, CZ-252 43 Pruhonice, Czech Republic
2 Department of Botany, Faculty of Science, Charles University, Benátská 2, CZ-128 01 Praha 2, Czech Republic

* For correspondence. E-mail: zuzmun{at}natur.cuni.cz

Received: 27 April 2007    Returned for revision: 15 June 2007    Accepted: 10 July 2007    Published electronically: 19 September 2007


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 SUPPLEMENTARY INFORMATION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 

Background and Aims: Despite the recent enormous increase in the number of studies on polyploid species, no studies to date have explored the population dynamics of these taxa. It is thus not known whether the commonly reported differences in single life-history traits between taxa of different ploidy levels result in differences in population dynamics.

Methods: This study explores differences in single life-history traits and in the complete life cycle between populations of different ploidy levels and compares these differences with differences observed between different habitat types and years. Diploid and hexaploid populations of a perennial herb, Aster amellus, are used as the study system. Transition matrix models were used to describe the dynamics of the populations, and population growth rates, elasticity values and life-table response experiments were used to compare the dynamics between populations and years.

Key Results: The results indicate that between-year variation in population dynamics is much larger than variation between different ploidy levels and different habitat conditions. Significant differences exist, however, in the structure of the transition matrices, indicating that the dynamics of the different ploidy levels are different. Strong differences in probability of extinction of local populations were also found, with hexaploid populations having higher probability than diploid populations, indicating strong potential differences in persistence of these populations.

Conclusions: This is the first study on complete population dynamics of plants of different ploidy levels. This knowledge will help to understand the ability of new ploidy levels to spread into new areas and persist there, and the interactions of different ploidy levels in secondary contact zones. This knowledge will also contribute to understanding of interactions of different ploidy levels with other plant species or other interacting organisms such as pollinators or herbivores.

Key words: Asteraceae, co-existence, contact zone, evolution, growth rate, LTRE, matrix model, permutation test, polyploidy, seed production


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 SUPPLEMENTARY INFORMATION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 
Polyploidy, a state of having more than two complete chromosome sets per nucleus, has played a key role in the evolution and diversification of the plant kingdom. It has been estimated that between 47 and 70 % of flowering plant species are the descendants of polyploid ancestors (Masterson, 1994; see also Soltis, 2005). Polyploid complexes have recently become the focus of many studies, resulting in an increasing amount of knowledge on performance of polyploid species. In many taxa, individuals of higher ploidy levels have higher seed production (e.g. Lindner and Garcia, 1997; Burton and Husband, 2000), larger inflorescences (Petit and Thompson, 1997), larger overall biomass (e.g. Petit and Thompson, 1997) and increased vigour as seedlings (Berdahl and Ries, 1997). There are, however, also studies showing no differences in mean traits between ploidy levels (e.g. Petit et al., 1996; Münzbergová, 2007).

Single species traits provide an indication of the differences in performance of individuals of different ploidy levels. The relative importance of the traits for long-term performance of a species cannot be estimated, however, without knowledge of the full life cycle of the species (Ehrlén, 2003; Münzbergová, 2005, 2006a). To understand differences in performance between different ploidy levels, it is thus necessary to study the complete life cycle of the species.

Many studies have shown that diploids and their polyploid relatives occupy different types of habitats (e.g. Tyler et al., 1978; Bayer and Stebbins, 1982; Jay et al., 1991), or that the two ploidy levels differ in the width of the habitat types occupied (e.g. Stebbins, 1950, 1985; Gornall and Wentworth, 1993). As a result, the differences in single plant traits observed in the field can result not only from differences in ploidy levels but also from the different habitat conditions. That is why most studies comparing traits of polyploid species pairs are carried out in the common garden (e.g. Berdahl and Ries, 1997; Münzbergová, 2007). While transplants in a common environment allow assessment of the effects of the ploidy level on different phenotypes, they are not appropriate for assessing population dynamics. Phenotypes are determined by environmental as well as genetic factors, and these environmental factors can play a decisive role in altering the effects of traits on population dynamics. Therefore, it is important that comparative studies of plant demography make use of natural habitats.

Studies on differences in population dynamics between plants of different ploidy levels can significantly enhance our understanding of factors affecting the spread and persistence of different ploidy levels within new areas and the interaction between different ploidy levels in secondary contact zones. This knowledge will thus provide a key to understanding polyploid evolution and success of polyploids in areas previously occupied by their diploid ancestors (Abbott and Lowe, 2004; Husband, 2004; Rausch and Morgan, 2005). Given the knowledge on wider distribution range, wider range of habitats occupied and higher individual growth of many polyploids compared with diploids, it is predicted that populations of polyploids will grow more rapidly, spread faster and rely more on generative reproduction than populations of diploids.

Knowledge of the population dynamics of diploid and polyploid species is also needed to evaluate the effects of different interacting organisms such as herbivores and pollinators on plants of different ploidy levels (e.g. Thompson et al., 1997; Husband, 2000; Münzbergová, 2006b). Studies that perform detailed demographic analyses to describe the complete life cycle of populations of different ploidy levels within the same species are, however, lacking.

This study aims to explore differences in life-history traits between diploid and polyploid individuals, and to understand the effect of these differences on population dynamics. Specifically, diploid and hexaploid populations of the perennial herb, Aster amellus L., were studied, and both single life cycle transitions and the full life cycle of the species were explored. In a previous study (Münzbergová, 2006b), it was shown that Coleophora obscenella, a monophagous seed predator, consumes more seeds from hexaploid plants than from diploid plants. The results of the current study will thus directly contribute to estimating the effect of the seed predator on the persistence of the plant populations.

The results of the study should provide information on differences in population dynamics of the different ploidy levels. The observed differences can be due to the polyploidization process per se or to differences in the evolutionary history of the two ploidy levels. Distinguishing between these two alternatives is, unfortunately, not possible unless artificially synthesized polyploids are used or unless several independent lineages of diploid–polyploid pairs within a single species are compared. Also, since this work is based on natural populations, the possibility cannot be excluded that the differences in population dynamics between the two ploidy levels are due to unidentified environmental differences between microsites occupied by the two ploidy levels. The study will thus provide information on differences in population dynamics between the two ploidy levels that can be due to any of the three processes.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 CONCLUSIONS
 SUPPLEMENTARY INFORMATION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 
Study species
Aster amellus L. is a perennial herb growing in open xerothermic habitats. Its European distribution range extends from northern Italy to Lithuania, and the southern distribution limit goes through northern Italy and Macedonia (Merxmüller et al., 1976). Outside Europe it extends to the Black Sea and to the northern Caucasus (Meusel and Jäger, 1992). Throughout its range it is known in three ploidy levels (di-, tetra- and hexa-) (Merxmüller et al., 1976). In the study area, the western part of the Czech Republic (Bohemia) is a contact zone between diploid and hexaploid individuals (Mandáková and Münzbergová, 2006). The populations of the two ploidy levels are partly geographically separated, with diploid populations prevailing on the west and hexaploid populations on the east. Because the two ploidy levels never co-occur in a single population, it was easy to estimate accurately the demographic parameters of the two ploidy levels separately, thereby eliminating potential reproductive interference that could alter seed production if the two ploidies were in sympatry. The species reproduces both sexually and clonally (pers. obs.).

Study localities
The study took place in northern Bohemia, a contact zone of the two ploidy levels within the Czech Republic. In a previous study, it was shown that while the diploid populations occur only in low-productivity habitats, hexaploid populations occur in both low and high-productivity habitats (Münzbergová, 2007). The species composition of the low-productivity habitats of the two ploidy levels does not differ, indicating that it is the same type of habitat (Mandáková and Münzbergová, 2006). For this study, nine different populations of the species were selected: three diploid populations and six hexaploid populations. The ploidy level of the populations was estimated using flow cytometry in a previous study (Mandáková and Münzbergová, 2006). The hexaploid populations differ in habitat productivity; three populations are in low-productivity habitats and three populations in high-productivity habitats. The populations correspond to those used by Münzbergová (2007); a detailed description of the localities is provided in Table 1. The distance between the single populations of different ploidy levels is between 1 and 15 km, and the furthest distance between the localities is 30 km. The localities of the three types are, however, still partly geographically isolated from each other (Table 1). The size of the populations estimated as the number of flowering ramets varies between 260 and 2600 individuals. Genetic comparison of the populations indicates limited gene flow between populations of the two ploidy levels (T. Mandáková and Z. Münzbergová, unpubl. res.).


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  		TABLE 1. List of localities used in the study

 
Survival and transitions across life stages
To describe the complete life cycle of the species, at least 150 individuals were marked (ramets) with at least 30 individuals in each stage (seedling, vegetative and reproductive) in each studied population in 2002. The minimum number of individuals per stage was set to assure that a more or less equal number of individuals in each stage was marked (see Münzbergová and Ehrlén, 2005). The individuals were marked in several permanent plots per locality (each plot was approx. 2 m2). Marking began with all individuals in one corner of the plot and proceeded across a diagonal to the opposite corner. When there were already 20 marked individuals of one stage in that plot, further individuals of this stage were skipped to ensure that each stage was represented by at least ten individuals per plot. Because the species reproduces clonally, a subplot was delimited (about 1 m2) within each plot, where all individuals were marked so that new clonal recruits could be recognized. Due to different spatial structures of the populations and thus different numbers of plots, number of individuals per plot and distances between plots, it was decided to merge the data from all plots within a single locality and not to take the plot structure into account when analysing the data.

Marking individuals in several plots per locality was a compromise between an attempt to cover different parts of the locality, to keep track of the marked plants and to recognize clonal recruits. Each individual was marked with plastic and metal labels that were placed just behind the plant. A census was completed every August from 2002 to 2005. Survival of each individual and its size were recorded. If there were fewer than 30 living, marked individuals per stage at the time of the census, new individuals were marked to maintain the minimum number of individuals per stage for the next transition period. At each census, the leaves and inflorescences were counted, and the length of the longest leaf was measured. All new clonal ramets were also recorded and marked.

Seedlings of A. amellus lose cotyledons in very early stages of development, and cotyledons can thus not be used to define seedlings. The maximum size that an individual could reach within 1 year in the field was thus used as a limit of the smallest category. These individuals also usually did not flower in the subsequent year. This category was defined as plants with leaves smaller than 3 cm. All larger vegetative individuals were placed in the second stage; also new vegetative ramets were considered at the second stage. Further splitting of this stage did not seem sensible due to the low variation in size of the vegetative plants. Reproductive plants were considered at the third stage.

Generative reproduction
Seedling reproduction was studied each year from 2002 to 2005 by counting the number of new natural seedlings per plot in plots used to follow plant performance. This number was divided by the number of flowering plants the year before in the same plots, and represented the number of new seedlings per flowering plant. This was possible because the permanent plots were situated within more or less continuous stands of A. amellus and it could be assumed that the number of seeds leaving the plots is approximately equal to the number of seeds arriving at the plots.

In a previous study (Münzbergová, 2004), it was found that 42 % of viable seeds survive in the seed bank over 3 years when buried underground. The same study, however, did not find delayed germination of seeds of this species when sown on the soil surface. As a result, seed was not included as a separate stage in the matrix model.

Single life-history traits
Before exploring the effect of ploidy level/productivity on the full life cycle of the species, their effect on single life-history traits within the life cycle of the species was investigated. To do this, first of all the effect of ploidy level/productivity on traits related to generative reproduction was explored: the number of initiated and developed seeds and seed germination (see Münzbergová, 2006b). Data on these traits were obtained in a different study that explored these traits in a wider range of A. amellus populations in the same region (Münzbergová, 2006b). For the purpose of this study, data were only used from the nine studied populations and 3 years (2002–2004). Furthermore, a comparison was made of data on several single life-history traits directly included in the transition matrices – probability of flowering, survival and clonal growth.

Data analysis
This study's design was not fully factorial because diploid populations occur only in low-productivity habitats. When analysing the data, two separate tests were thus always performed: a test of the effect of ploidy level on populations from low-productivity habitats and a test of the effect of home environment on hexaploid populations. In each case, the strength of these two effects was then compared. To take into account that these two tests were not fully independent, the conventional {alpha} level was reduced from 0·05 to 0·025 to estimate significance.

Comparison of single life-history traits
First, the effect of ploidy level/productivity on germination and number of initiated and developed seeds was tested using analysis of variance (ANOVA). Ploidy level/productivity, year, locality nested within ploidy level/productivity and their interactions were used as independent variables. The residuals of the analyses were normally distributed and no transformation of the dependent variables was thus necessary.

Furthermore, the effect of ploidy level/productivity on probability of flowering, survival and clonal growth was tested. These parameters were determined in individuals of different sizes. To remove this effect, the stage in the previous year was used as another independent variable in the tests. In all cases the data were collected in three time periods and thus year was used as another independent variable. A test was also made of the effect of locality nested within ploidy level/productivity and explored all the second- and third-order interactions. No third-order interactions were, however, significant and are thus not reported. All the data from a single locality were pooled together and the plot structure was not taken into account (see above). The effect of these independent variables on probability of flowering and survival was tested using logistic regression. The effect on clonal growth (number of clonal offsprings per individual per year) was tested using a generalized linear model assuming Poisson distribution of the dependent variable.

To take into account that individuals from a single population were not independent, the ploidy level/productivity effects and the interaction of ploidy level/productivity and year/stage previous year were tested in all the above tests against locality and locality x year/stage previous year, respectively.

Population performance
Demographic data were examined using transition matrix models (Caswell, 2001). Analysis of a transition matrix yields a finite rate of increase, {lambda}, of the population. Analyses of projection matrices also generate information on the change in population growth rate, {delta}{lambda}, following a small change in aij ({delta}aij), sensitivity. Proportional sensitivity, elasticity, is usually used as a measure of the contribution of a matrix element to fitness (de Kroon et al., 2000).

In this study, the finite rate of increase, {lambda} (population growth rate), was calculated for each population and transition interval. The pattern of elasticities was also calculated for each of the matrices. Because individuals were added to demography plots each year and the study was shorter than the life span of the species, the data on population dynamics do not take into account the covariance between different stages across transition intervals (Kalisz and McPeek, 1992).

Each estimate of transition probability and thus each estimate of population growth rate as well as of elasticity is confined with an error, because of the limited number of individuals that can be sampled. To estimate this error, bootstrap confidence intervals were calculated (Alvarez-Buylla and Slatkin, 1994) of the population growth rate and elasticity of each population. This was done by bootstrapping the original data used to derive the transition matrices 10 000 times. Based on the results, confidence intervals of population growth rates and elasticities were constructed for each population and year (Efron and Tibshirani, 1994). To do this, a MATLAB script developed for the purpose of a previous study was used (Münzbergová, 2006a).

The confidence intervals allow estimation of variation in the single parameters, but do not provide estimates of significance of the differences between the transition matrices (Caswell, 2001). To estimate this, a permutation test was performed, permuting single individuals used to estimate transition probabilities between each pair of populations. Data used to estimate intensity of clonal growth and of reproduction were also permutated. In each permutation run the difference in population growth rate between the pair of populations was estimated and a count was made of the number of permutation runs in which the absolute value of the difference was larger than the observed difference. This value was then used to estimate the probability that the observed difference between each pair of demographic matrices could be just random. In each case, 10 000 permutation runs were used. To do this, a MATLAB script developed for the purpose of this study was used.

Furthermore, the stochastic simulation approach (Caswell, 2001) was used to combine all the matrices of one type (diploid, hexaploid from low and high-productivity habitats) and estimate overall population growth rate of these combined matrices. The bootstraped matrices for this combination were also used, and confidence intervals of the overall population growth rate of each type of population were created (see Münzbergová, 2005). To demonstrate the effect of the overall population growth rate for survival of populations of each type, populations of 100 flowering individuals were projected by randomly drawing one of the nine matrices of each type (3 localities x 3 transition intervals) in each time step, multiplying a population vector with this matrix, and evaluating population survival after 20 and 50 years. In each step, the resulting population vector was replaced by values drawn from Poisson distribution with the given mean to simulate demographic stochasticity. This projection was repeated 10 000 times for each type (Münzbergová, 2005).

A life-table response experiment (LTRE) with fixed factorial design was conducted to examine the effect of ploidy level/productivity and year on population growth rate. LTRE is a form of retrospective analysis that allows quantification of factors responsible for the observed variation in population growth rate. Compared with elasticity analysis, the LTRE analysis quantifies the observed effects of single matrix elements on observed variation in population growth rate, and not expected effects. The approach described in Caswell (2001) was followed, and the mean matrix (A··) was calculated. Population growth rate was expressed as follows:


Formula 204M1

(1)
where {lambda}·· is the population growth rate of the mean matrix A··, and the effects of {alpha}p and ßy are the main effects of the pth level of ploidy level/productivity (diploid and hexaploid and low- and high-productivity, respectively) and the yth level of transition period (2002–2003, 2003–2004 and 2004–2005) on population growth rate {lambda}. The contribution of the transition aij to the effect of ploidy level/productivity and year on population growth can be expressed as follows:


Formula 204M2

(2)


Formula 204M3

(3)


Formula 204M4

(4)
Here, sij is the sensitivity of the ijth transition. Two types of sensitivity were used in this calculation. First, sensitivity matrices were evaluated half way between the particular treatment matrix and the mean matrix as suggested, e.g. by Brys et al. (2004). The advantage if this technique is that it takes into account differences in the sensitivity structure between the different treatments. On the other hand, the results of this decomposition are not fully additive. The analysis was thus also repeated using sensitivity of the mean matrix. Because the results of the two types of analyses did not differ qualitatively, only the latter results are presented.

The LTRE analysis indicates the contribution of each life cycle transition to differences between different levels of each factor (ploidy level/productivity, year). Important life cycle transitions are those with large positive contributions at some factor levels and large negative contributions at others. Analogously to ANOVA, the mean of the treatment effects is zero. The interaction term {alpha}ßpy is calculated as the difference between the actual contribution of aij to {lambda}py and the difference predicted on the basis of the additive model. Hence, a positive contribution indicates that this interaction increases {lambda}py above the value predicted by the additive model (Caswell, 2001).

Despite the fact that the LTRE is an analogy of ANOVA, almost no studies attempt to provide a test of significance of LTRE. An attempt was made to do this by performing a permutation test in which individuals were permutated between the categories being compared (in the same fashion as in the permutation test above), and repeating the LTRE using these permuted data. It was then calculated how often the overall contribution and the contribution of each matrix element is bigger than would be expected if the individuals were distributed among groups at random. This value was used as a significance value to identify the matrix elements that significantly contribute to differences between the categories being compared. A MATLAB script was used to perform the analysis, and 10 000 permutations were used in each case.

In a previous study, it was shown that the hexaploid plants suffer from greater herbivore damage than the diploid plants (Münzbergová, 2006b). In spite of this, the final seed production of the hexaploid plants was higher than that of diploid plants. Because the reduction in seed production may have a different effect on the two ploidy levels, the changes in population growth rates of the different ploidy levels due to changes in seed production were examined. To do this the transition matrices were selected and the reproductive transition (a13) was multiplied by values between 0 and 2, simulating both a reduction and an increase in seed production. This was done for the original as well as bootstrap matrices, and the stochastic simulations were used to calculate mean {lambda} for each ploidy level and habitat type, as well as to construct the confidence intervals of the values.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 CONCLUSIONS
 SUPPLEMENTARY INFORMATION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 
There were no significant differences between the two ploidy levels or habitat productivities in seed germination and number of initiated and developed seeds. The only exception is a marginally significant positive effect of ploidy level on the number of initiated seeds, with hexaploid plants having more seeds (Table 2). There were, however, strong significant differences between localities and between years, as well as several marginally significant interactions between locality and year in both groups of tests (Table 2).


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  		TABLE 2. Effect of year, ploidy level/productivity, locality nested within ploidy level/productivity and their interactions on seed germination, number of initiated and number of developed seeds

 
There were no significant differences in flowering, survival and clonal growth between the two ploidy levels, and no differences between populations from habitats differing in productivity (Table 3). There were also no significant interactions between ploidy level/productivity and year and stage (Table 3). In contrast, there were significant differences in survival and probability of flowering, but not in clonal growth between single localities (Table 3) in both groups of tests. The effect of locality also significantly interacted with stage and with year (Table 3).


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  		TABLE 3. Effect of year, stage in the previous year, ploidy level/productivity, locality nested within ploidy level/productivity and their interactions on probability of flowering, survival and clonal growth

 
There was a high level of variation between transition matrices from different years and localities (see Supplementary information 1, available online). The high variation between matrices resulted in a high variation in population growth rates (Fig. 1). Population growth rate varied between both years and populations, but there were no clear trends in either of the two. There were also no obvious differences between the two ploidy levels and the two habitat types (Fig. 1). Out of 27 matrices, nine had a population growth rate significantly lower than 1, while two had a population growth rate significantly higher than 1. All the others did not differ significantly from 1 (Fig. 1).


Figure 1
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  		FIG. 1. Population growth rate of diploid and hexaploid populations from low and high-productivity habitats separately for each population and transition interval with 95 % confidence intervals. Different letters within bars from single population indicate significant between-year differences. The horizontal line indicates {lambda} = 1, i.e. stable populations.

 
Stochastic population growth rate, describing the population growth rate of all the matrices within each type combined, did not differ much between the three types of populations. The mean stochastic growth rate in diploid populations was 0·97 (95 % confidence interval 0·95–1·00), in hexaploid populations from low-productivity habitats it was 0·93 (0·91–0·96) and in hexaploid populations from high-productivity habitats it was 0·93 (0·91–0·95). These differences, however, resulted in relatively large differences in survival probability of populations of the different types. A population of 100 flowering individuals of diploids had 0·4 % probability to become extinct in 20 years and 27 % probability to become extinct in 50 years. For hexaploid populations in low-productivity habitats, the probabilities were 4·5 and 70 %; for hexaploid populations in high-productivity habitats they were 4 and 70 %.

Similar to the transition matrices themselves, high between-population and between-year variations could also be seen from the analysis of elasticity (see Supplementary information 2, available online). In spite of this high variation, several common trends could be identified. First, the most important transition was transition a22, i.e. the transition of survival of vegetative individuals and clonal growth. This transition was followed by all the other transitions between vegetative and flowering individuals (a23, a32 and a33). This means that clonal growth, and growth and survival of vegetative and flowering plants were much more important for population dynamics of the species than generative reproduction and seedling survival.

When comparing the elasticity of matrices of the three types (matrices within type combined using stochastic simulations), several significant differences emerged (Fig. 2). Diploid populations had higher elasticity of the a22 transition than hexaploid populations from high-productivity habitats; hexaploid populations from low-productivity habitats were in between the two. Furthermore, diploid populations had lower elasticity of transitions a23, a31 and a32 compared with both groups of hexaploid populations. Finally, the elasticity of transition a33 was significantly higher in populations from low-productivity habitats (both 2x and 6x), than in populations from high-productivity habitats (Fig. 2). All this showed a gradual change in structure of the matrix from diploid, via hexaploid populations from low-productivity habitats to hexaploid populations from high-productivity habitats. Along this gradient, the importance of survival of vegetative plants and clonal reproduction of vegetative plants was decreasing, while the importance of flowering plants was increasing (Fig. 2).


Figure 2
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  		FIG. 2. Elasticity of single life cycle transitions for diploid populations (2xL), hexaploid populations from low-productivity habitats (6xL) and hexaploid populations from high-productivity habitats (6xH) with 95 % confidence intervals. The values were obtained using stochastic simulations. The plots within the figure are arranged in a form of a transition matrix. Different letters within the single plots indicate significant differences. (de Kroon et al., 2000)

 
The LTRE analysis indicated a relatively low contribution of ploidy level and habitat productivity to the observed variation in population growth rate (Table 4). The permutation tests suggested that overall these contributions were not significant (Table 4). When decomposed into single matrix elements, the population growth rate of diploids was significantly more driven by generative reproduction (transition a13), and by survival of vegetative individuals and by clonal growth (transition a22, Table 5). The population growth rate of the hexaploid populations, however, was driven mainly by the growth of vegetative plants to the flowering stage (transition a32, Table 5). When comparing population dynamics of plants from low and high-productivity habitats, the only significant difference was the higher contribution of generative reproduction (transition a13) and survival of flowering individuals (transition a33) to population growth rate in high-productivity habitats.


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  		TABLE 4. Contribution of ploidy level/productivity, year and population to the observed variation in population growth rates of Aster amellus determined using life-table response experiments (LTREs)

 


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  		TABLE 5. The contribution of each vital rate to the effect of ploidy level/productivity and year on population growth rate estimated using LTRE analysis (see Materials and Methods)

 
LTRE analysis using data from low-productivity habitats only indicated no significant contribution of year to observed variation in population growth rate (Table 4). In contrast, in the data set containing only hexaploid individuals, the second year had significant negative and the third significant positive effects (Table 4). The between-year variation was significantly affected by all the transitions, except for the rare transition a31 and the growth transition a23, at least in some cases (Table 5).

Comparison of the effect of changes in seed production on population growth rate indicated that the change was the highest in hexaploid populations from high-productivity habitats (slope 0·0219), followed by diploids (slope 0·0207) and hexaploids from low-productivity habitats (slope 0·0156, see Supplementary information 3, available online). The differences between slopes, were, however, not significant.


   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
CONCLUSIONS
 SUPPLEMENTARY INFORMATION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 
This study's results indicated no significant differences in mean population growth rate between diploid and hexaploid populations of A. amellus. The different ploidy levels, however, differed in extinction probability of local populations, with hexaploid populations having higher extinction probability than the diploid populations. Furthermore, there were significant differences in the matrix structure between the different types as identified using the elasticity analysis, with diploid populations relying more on clonal reproduction and survival of vegetative plants and less on survival of flowering individuals. In most comparisons the hexaploid plants from low-productivity habitats were in between the diploid plants (all from low-productivity habitats) and hexaploid plants from high-productivity habitats, indicating that both ploidy level and habitat type determine differences between populations.

The absence of significant effects of ploidy level on mean population dynamics and lower overall performance of the hexaploid populations due to higher between-year variation apparently contrasted with the higher seed production in hexaploid plants found in this study as well as in the study of Münzbergová (2006b). It also contrasted with conclusions of many others who showed higher values of different traits in higher ploidy levels (e.g. Lindner and Garcia, 1997; Burton and Husband, 2000). The result, however, confirmed the conclusion of Ehrlén (2003) and Münzbergová (2005, 2006a) that significant differences in single traits do not necessarily mean significant differences in population dynamics. This inconsistency was due to different elasticity structure within the matrices of the different types.

In this study, no significant differences in population dynamics of single populations from the two environments were found. In this case, extinction probability was also comparable between the types. When looking at the elasticity patterns, the hexaploid populations from low-productivity habitats were in between the diploid populations and hexaploid populations from high-productivity habitats, indicating that habitat productivity at least partly affected the structure of the transition matrix. The differences between the different habitat types were, however, lower than in other studies (e.g. Oostermeijer et al., 1996; Freville et al., 2004; Vega and Montana, 2004; Jongejans and de Kroon, 2005). The conclusions on the lack of differentiation between habitats were in concordance with the previously observed high plasticity of A. amellus (Münzbergová, 2007).

Similarly to analysis of population growth rate, the LTRE analysis did not indicate a significant difference in the overall contribution of ploidy level to the observed variation in population growth rate. In agreement with the elasticity analysis, few matrix elements contributing differently to population growth rate of the two ploidy levels were, however, identified in the LTRE analysis. This supported the above statement that the structure of the matrices was different between the ploidy levels. A similar result was found for habitat productivity.

When comparing the life cycle transitions that differentiated the populations in the prospective analyses (elasticity) and in the retrospective analyses (LTRE), it was clear that these two types of analyses do not fully match. Specifically, generative reproduction was identified as a trait that contributed to the observed variation in population growth rate of the different ploidy levels, whereas the elasticity of this transition was not different between the types. This corresponds to the previously reported inconsistency of conclusions one can obtain using these two types of analyses (Caswell, 2000). In this study, the inconsistency between the prospective and retrospective analyses could be explained by high variation in generative reproduction between populations and years.

Contrary to the absence of significant overall differences between ploidy levels/productivity, differences between years were high and often significant. This was in agreement with many previous studies on plant population dynamics that showed high between-year variations in performance of plant populations (e.g. Eriksson and Eriksson, 2000; Pfeifer et al., 2006). This pattern could also be seen in the elasticity and LTRE analyses.

In the study an attempt was made to estimate confidence intervals of the observed parameters and express the significance of the differences between different categories. While such estimates are standard parts of most ecological studies, they are still not common in studies on population dynamics (e.g. Damman and Cain, 1998; Griffith and Forseth, 2005). Recently authors have started estimating reliability of single estimates of population growth rate (e.g. Nordbakken et al., 2004; Weppler et al., 2006). Studies performing a test of significance in elasticity and LTRE are, however, largely lacking (e.g. Brys et al., 2004; Griffith and Forseth; 2005; but see Colling and Matthies, 2006). In this study, it was shown that many apparent differences between categories were not significant. Without such quantification of the reliability of the estimates, it could falsely be concluded that the ploidy levels and different habitat types importantly contribute to observed variation in population growth rates. The magnitude of the differences between population growth rates of different populations largely corresponded to differences observed between populations of a single species reported elsewhere (e.g. Ehrlén, 1995; Jongejans and de Kroon, 2005).

The differences in structure of the projection matrices between the different ploidy levels indicated that the overall growth strategy of the different ploidy levels was different, with hexaploid plants relying more on growth into flowering stage and diploid populations relying more on reproduction, clonal growth and survival. The observed differences in population dynamics between the two ploidy levels were generally small but, together with different structure of the matrices, lead to large differences in extinction probability. Specifically, hexaploid populations had higher extinction probability than diploid populations. All this suggested that populations of hexaploids are less persistent but have overall the same ability to grow. Higher local extinction probabilities are characteristic of species with a shorter life span and faster spread at the landscape level (Silvertown et al., 1993). Given that the hexaploid populations had the same overall population growth rate as diploid populations, the hexaploid populations could be considered as more dynamic populations with higher potential ability to colonize new habitats. This is only partly in agreement with the prediction that population dynamics of higher ploidy levels should rely more on generative reproduction and have higher population turnover. Still, higher extinction probability linked with the same population growth rate indicates that the hexaploid populations are more dynamic. Such differences can have important implications for spread of the two ploidy levels across a secondary contact zone and thus for long-term performance of populations of these two ploidy levels in the landscape.

These differences might also influence the conclusions of studies on between-ploidy level interactions that are usually concerned just with patterns of between-ploidy level mating and viability of offspring resulting from these crosses in early phases of growth (e.g. Abbott and Lowe, 2004; Husband, 2004; Rausch and Morgan, 2005).

The results exploring the effect of changes in seed production on population growth rate indicated that hexaploid plants from high-productivity habitats are the most sensitive, while the hexaploid plants from low-productivity habitats were the least sensitive and diploid plants were intermediate. The difference in the slope, was, however, not significant. This indicated that effects of seed herbivory on the ploidy levels described by Münzbergová (2006b) are comparable between the ploidy levels.

The observed differences between the two ploidy levels could be due to several possible mechanisms. First, the difference could be due to the polyploidization event per se. Polyploidization affects the amount of nuclear DNA and leads to an increase in cell volume of the organism (e.g. Van't Hof and Sparrow, 1963; Evans and Rees, 1971) having direct consequences on various plant functions possibly affecting performance of the populations. Secondly, the differences between the ploidy levels might be caused by different evolutionary history. Such a difference could arise in cases of secondary contact zones, as is the situation assumed in the present species. While it would be interesting to distinguish between these two possible explanations, this is not possible without comparison of population dynamics of artificially synthesized polyploids or comparison of diploids and polyploids of several independent genetic lineages within single species. Thirdly, the differences might be related to differences in habitat conditions at sites occupied by the two ploidy levels. While it has been shown in a previous study that the two ploidy levels do not differ in habitat at a larger spatial scale (Mandáková and Münzbergová, 2006), the environmental differences between the two ploidy levels cannot be completely excluded because the localities of the three types were partly spatially separated in the study region.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
SUPPLEMENTARY INFORMATION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 
The results of this study indicated that while there were no significant differences in mean performance of populations of the different ploidy levels, the overall dynamics of diploid and hexaploid populations were different. Specifically, the diploid populations were more stable and thus have a lower probability of local extinction. Also the structure of the transition matrices as described using both prospective (elasticity) and retrospective (LTRE) analyses was significantly different between the two ploidy levels. All this indicated that single traits cannot be easily used to compare performance of populations of different ploidy levels, and the common assumption on better performance of higher ploidy levels does not have to be true.

The results also suggested that between-year variation resulted in much larger changes in population growth rate than ploidy level or habitat productivity. The variation in the structure of the transition matrices due to ploidy levels, habitat types and years was, however, largely comparable. This indicated that ploidy level could significantly alter population dynamics at least to the same extent as habitat type and year.

This is the first study on full population dynamics of plants of a different ploidy level. The results are thus hard to generalize, and more studies are needed before it will be possible to reach general conclusions about the dynamics of populations of different ploidy levels. The obtained knowledge is expected to provide a valuable contribution to our understanding of the spread and survival of new ploidy levels into new areas and the dynamics on secondary contact zones between different ploidy levels. Until now, studies have been concerned only with differences in single traits between different ploidy levels without specific knowledge of the consequences of these single trait differences for long-term population dynamics. The results of this study indicated that the differences in single traits between the ploidy levels cannot be easily used to deduce differences in population dynamics between them.


   SUPPLEMENTARY INFORMATION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 SUPPLEMENTARY INFORMATION
ACKNOWLEDGEMENTS
 LITERATURE CITED
 
Supplemetary information is available online at http://aob.oxfordjournals.org/, as follows. (1) Transition matrices from nine populations and three transition periods used in the study; (2) elasticity of single life cycle transitions in the different populations and years with 95 % confidence intervals; and (3) effect of changes in seed production on population growth rate of populations of different ploidy levels and from habitats of different productivity.


   ACKNOWLEDGEMENTS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 SUPPLEMENTARY INFORMATION
 ACKNOWLEDGEMENTS
LITERATURE CITED
 
I would like to thank Tomás Herben and two anonymous reviewers for comments on the previous version of the manuscript, and Janice Forry for language revision. This study was supported by grant GACR 206/06/0598. It was also partly supported by GAAV B6111303, MSMT 0021620828 and AV0Z6005908.


   LITERATURE CITED
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 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 CONCLUSIONS
 SUPPLEMENTARY INFORMATION
 ACKNOWLEDGEMENTS
 LITERATURE CITED
 

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