Plant material
Because of limited resources we had to make a choice between sampling several stands for both management systems at a low level of individual resolution, since experimental effort is particularly large for forest tree species with a very low density, or to concentrate on an exhaustive survey of one exemplar of each system. We had to decide in favour of the latter, since locally complete surveys are required for reliable estimates of degrees of clonal reproduction. For this reason, the present study is to be understood as a first attempt to test common hypotheses on the effects of different management types on the breeding system of wild cherry and to infer more realistic hypotheses from these observations.
Two P. avium stands near Göttingen in Germany were chosen, both of which are spatially isolated from other occurrences (because of larger surrounding agricultural areas). The two stands originate from natural regeneration but have been subjected to different silvicultural treatments. All wild cherry trees were sampled within these two stands (figure 2) in order to avoid effects of differences in sample size on the accuracy in allele frequency estimates and thus the method of clonal identification in each plot.
One of the chosen stands is a mixed stand near the village of Wibbecke that consists of 78 wild cherry trees that are about 100 years old. These cherry trees are scattered among a mixture of predominantly sessile oak (Quercus petraea) and hornbeam (Carpinus betulus) as well as sporadically occuring Norway maple (Acer platanoides), field maple (Acer campestre) and wild service tree (Sorbus torminalis). Altogether, the area of the stand covers more than 10 hectares. Referring to historical evidence, the trees had been managed as CWS until the beginning of the last century. This is also the reason for the almost total absence of beech (Fagus sylvatica). The forest management plan of 1991 mentioned that most of the wild cherry trees might be asexually regenerated by coppicing.
The second wild cherry stand (56 trees on about 5 hectares) near Roringen is about 70 years old and located in a protection area that is treated as a high-forest system. The consequence is that the area is mostly dominated by beech, although the environmental conditions are very similar to Wibbecke (chalcerous soil). Additional scattered tree species are common ash (Fraxinus excelsior), hornbeam (C. betulus), Norway maple (A. platanoides), field maple (A. campestre) and, very scattered, wild service tree (S. torminalis). The observed tree mixture is representative for the group of mesophyllic chalcerous beech forests.
DNA extraction and visualization of amplified SSR (microsatellite) fragments
DNA was purified from fresh leaf material using the QIAGEN DNeasy96 Plant Kit and tested on a 0.8% agarose gel. For standard population genetic studies six nuclear microsatellites were analysed, as described in table 1. Amplification was carried out in a PTC-200 (MJ Research) using labeled primers with green (HEX) or blue (FAM) flourescent dyes. The Polymerase Chain Reaction (PCR) was performed in a 10 μl reaction volume containing 10 ng template DNA, 1.5 mM MgCl2, 10 mM Tris-HCl pH 9.0, 50 mM KCl, 0.15 mM of each dNTPs (QIAGEN), 0.5 units of HotStarTaq™ DNA polymerase (QIAGEN) and 0.2 μM of each primer. SSR fragments were visualized on the ABI PRISM 3100 Genetic Analyser (Applied Biosystems/HITACHI) and analysed using GeneScan 3.7 and the Genotyper 3.7 computer software. Since this investigation was no large-scale genotyping project, we manually checked all the automatically processed genotypes in order to exclude errors of PCR product size analyses (problems for high-throughput see [23]). The SSR allele sizes in our study could be determined uniquely.
Measurement of genetic diversity
To give an idea about the range of genetic variation available for the analysis of clonal propagation, the effective number of alleles [24], the gene pool diversity [25] and the hypothetical gametic diversity [26] are communicated. These parameters give hints as to the efficiency of clone identification in the sense that higher diversity values are generally expected to detect existing clones with higher probability.
Statistical and conceptual considerations
Testing for clonal reproduction
The testing procedure for clonal propagation is based on the idea that exclusively sexual reproduction of a genotype is unlikely, if its observed frequency exceeds a specified threshold. The (hypothetical) threshold frequency is argued to typically not be exceeded in a population with specified frequencies of the genes represented in the genotype, and in which this genotype is exclusively sexually produced. Hence, given the threshold frequency for the genotype, the hypothesis that all of the copies of the genotype observed in a sample result from sexual reproduction is rejected if the number of copies is too large. More precisely, the hypothesis is rejected if the probability CnN(H) of finding the observed number n or more copies of the genotype in a sample of size N and for given (hypothetical) threshold frequency H is smaller than a given significance level ε, i.e. if
In essence, CnN(H) ε rejects the hypothesis that the frequency of the genotype in question is equal to or smaller than the threshold frequency H. Rejection of the hypothesis thus implies that at least two copies of the genotype can be assumed to belong to the same clone. Hence, if additional gene loci are considered in the sample and if at these loci up to n - 1 different genotypes are found, this is still in accordance with the rejected hypothesis. By definition, the hypothesis is not rejected, and thus exclusively sexual reproduction of the genotype is assumed for all threshold frequencies H for which CnN(H) ≥ ε[10].
Testing genotype copies for representing a single clone
In most cases, as in the present paper, the focus is set on knowing whether all of the copies of a genotype observed in a sample could belong to the same clone. This hypothesis is accepted if any two individuals which carry copies of the genotype are unlikely to belong to different clones (genets), i.e. if C2N(H) ε (see bottom of figure 3, for the underlying theory see [10]). Hence, C2N(H) ≥ ε implies that the hypothesis cannot be rejected that two of the copies of the genotype belong to different clones including the case where all copies result from sexual reproduction. In the current literature, the almost exclusively considered case of sexual reproduction is specified by complete random association of genes such that the threshold frequency H of the target genotype results from multiplication of the frequencies of those alleles that are represented in the genotype [10]. Because of this fact our analysis will start with this assumption of the threshold frequency H and will later on check its appropriateness.
Utilizing Type one errors in the assessment of gene associations
As was explained in the introduction, the assumption of random gene association as a characteristic of sexual reproduction is generally difficult to justify. Thus, the rejection of sexual reproduction of a set of individuals with identical multilocus genotypes may be erroneous if the assumption on gene association is incorrect. Accepting clonal propagation of a genotype could in this case be an error. This is called a Type one error, and it erroneously rejects the hypothesis of sexual reproduction.
Sexual reproduction is characterized by a specific threshold frequency of a genotype under consideration, as explained above. Therefore, if a Type one error is committed, this is due to an inappropriate characterization of sexual reproduction as determined by the threshold frequency. A major problem in the assessment of gene associations at multiple loci results from limited sample sizes in relation to the very small frequencies expected for multilocus genotypes. Therefore we developed a non-conventional approach to assessing gene associations that does not directly depend on frequency estimates of genotypes:
The possibility of committing a Type one error under the hypothesis of random association of genes in genotypes is checked in the present paper by additionally considering two microsatellite loci, which were scored in the stand of Roringen in connection with a different study, and six polymorphic isozyme systems (pgm, idh, 6-pgdh, skdh, got and aco) in the stand of Wibbecke, which were studied earlier by [27]. Detection of a Type one error with the help of these loci and on the basis of C2N(H) will then give rise to the reconsideration of random association of genes as an appropriate specification of the threshold frequency H. As was explained above, in this reconsideration H must be large enough to guarantee C2N(H) ≥ ε, and, in order to be admissible, it must respect the constraints set by the allele frequencies in the population. Taking account of these constraints, genotype frequencies can be expressed as a function of the frequencies of those alleles represented in the genotype and of a consistently definable measure Ar(g) of relative gene association (see figure 3). Ar(g) varies between -1 and +1 and becomes zero exactly for the case of random association of all genes representted in genotype g.
For given gene frequencies, the (hypothetical) frequency H(g) of a genotype increases strictly with the measure Ar(g) of gene association, as does the significance probability CnN(H) for each fixed n and N. Hence, as Ar moves from -1 to +1, the significance probability C2N may cross the significance level ε, so that for small Ar exclusively clonal propagation is inferred and for sufficiently large Ar sexual reproduction cannot be rejected in producing the observed copies of the genotype. Consequently, if the hypothesis of exclusively clonal propagation is accepted under a special assumption on Ar (Ar = 0 say, as is common usage) and if consideration of additional genetic traits reveals genetic variation within the supposed clone, then a Type one error is detected that is likely to be due to an inappropriate specification of Ar. In conclusion, a higher degree Ar of gene association must be assumed to avoid at least the detected Type one error, and this degree must be large enough to yield a threshold genotype frequency H for which C2N(H) ≥ ε. The thus obtained value of Ar is likely (on a level 1 - ε of likelihood) to constitute a lower bound for the degree of gene association characteristic of the observed genotype.
The principle of this approach of assessing degrees of gene association can be extended by picking one of the studied gene loci and considering it as an "additional" locus in the above sense, while the remaining loci are used for the primary characterization of multilocus genotypes. If one of these genotypes is observed in n ≥ 2 copies, which however differ at the "additional locus", the smallest value of Ar can be determined such that for the corresponding hypothetical threshold frequency H one obtains C2N(H) ≥ ε. This value of Ar specifies a lower bound for the degree of gene association of the target genotype on a level 1-ε of likelihood.
Mutation is, of course, another explanation of detecting genetic differences when considering additional gene loci. In this case it would be erroneous to conclude a Type one error, and the above method of estimating degrees of gene association would be without substance. In our study, however, we analysed tissue samples of several branches per adult tree without finding any genetic variation within trees. This leaves us with the possibility of mutation in primordial cells of the root. It would therefore require very large numbers of ramets of one clone in order to reach a sizable probability of detecting a mutational event. Such numbers of genetically identical individuals are not observed in our study. It is thus not reasonable to consider mutation as a significant force in our study.
Determination of the degree of clonal propagation
The degree of clonal propagation is measured as the average number of individuals (ramets) per clone or genet, where non-cloned individuals count as one clone or genet (N/G, with N = number of individuals and G = number of clones or genets). The occasionally reciprocal G/N is used in place of N/G (see e.g. [17,28]). Because of its higher intuitive appeal we however prefer the average number of ramets per genet as a measure of the individual genet cloning success.
On the stand level we used Simpson's index C of concentration (see [29], p. 309) for measuring the degree to which a stand results from clonal reproduction. This parameter calculates the probability that two individuals (drawn randomly from a population of N individuals without replacement) are identical in their multilocus genotypes: C = {[ni (ni - 1)]/[N (N - 1)]}, where ni is the number of individuals of genotype i and N is the total number of individuals in the population. Thus, C = 1 if the whole stand consists of one genet (clone) and C = 0 in the absence of clonal propagation.
Authors' contributions
This paper is the result of intense cooperation between both authors on all topics. AMH carried out field work as well as molecular genetic studies. AMH and HRG participated in the design of the study and in the performance and interpretation of the statistical analysis. Both authors read and improved the final manuscript.
Acknowledgements
This study was funded by the Deutsche Forschungsgemeinschaft (DFG), No. GR 435/22-1. We thank D. Kownatzki and E. Gillet for their constructive discussions and valuable ideas. Further we want to note that the suggestions and commends of three anonymous reviewers were of considerable help to improve the presentation of our results.
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