Academia.eduAcademia.edu

Figure 3 – uploaded by Sophie Arnaud-Haond

See full PDFdownloadDownload figure
Table 3 Influence of the sampling area geometry on the estimation of the number of genotypes (G) and genotypic richness (R), on the importance of edge effect (E,) and on its significance tested with a 1000 random resampling procedure (number Of P(ohserve srandom) < 9-05 in 10 tests; NS when none of the values was significant). An extrapolation procedure was used, based on the large rectangular sampled area of Cymodocea nodosa in Alfacs Bay (Alberto et al. 2005), to generate a high resolution virtual population with a similar clonal structure. Ten subsampling areas (about 50 m2) of each of the four following geometric shapes: circular (r = 4 m), squared (7 x 7 m), rectangular (14 x 3.5 m) or almost linear (38 x 1.3 m or 20 x 2.5 m), in which 30 sampling units were assigned random coordinates, were randomly set in the virtual population *Number of E, values significant (P < 0.05) after 10 resampling tests (1000 repetitions). NS when none of the 10 tests was significant

Table 3 Influence of the sampling area geometry on the estimation of the number of genotypes (G) and genotypic richness (R), on the importance of edge effect (E,) and on its significance tested with a 1000 random resampling procedure (number Of P(ohserve srandom) < 9-05 in 10 tests; NS when none of the values was significant). An extrapolation procedure was used, based on the large rectangular sampled area of Cymodocea nodosa in Alfacs Bay (Alberto et al. 2005), to generate a high resolution virtual population with a similar clonal structure. Ten subsampling areas (about 50 m2) of each of the four following geometric shapes: circular (r = 4 m), squared (7 x 7 m), rectangular (14 x 3.5 m) or almost linear (38 x 1.3 m or 20 x 2.5 m), in which 30 sampling units were assigned random coordinates, were randomly set in the virtual population *Number of E, values significant (P < 0.05) after 10 resampling tests (1000 repetitions). NS when none of the 10 tests was significant

Related Figures (13)

Fig. 1 (a) Time course of the number of studies on clonal plants using molecular markers per year, among the 247 published studies on clonal plants reviewed (bars), and the temporal evolution of the percentage of studies using allozymes (—), multibanding (RAPDs, AFLP and fingerprints; ---) and microsatellites (---). (b) The distribution of clonal diversity (R) estimated with Allozymes, Fingerprints (RAPDs, AFLP), and Microsatellites markers over the 297 studies reviewed, presented as the average (+ SE) for the studies using different marker types on the left panel, and as the cumulated frequency of increasing R-values on the right panel with lines pointing at the median values of R for different marker types.
Fig. 1 (a) Time course of the number of studies on clonal plants using molecular markers per year, among the 247 published studies on clonal plants reviewed (bars), and the temporal evolution of the percentage of studies using allozymes (—), multibanding (RAPDs, AFLP and fingerprints; ---) and microsatellites (---). (b) The distribution of clonal diversity (R) estimated with Allozymes, Fingerprints (RAPDs, AFLP), and Microsatellites markers over the 297 studies reviewed, presented as the average (+ SE) for the studies using different marker types on the left panel, and as the cumulated frequency of increasing R-values on the right panel with lines pointing at the median values of R for different marker types.
When the same genotype is detected n times ina sample of N sampling units, the probability that the repeated genotypes originate from distinct sexual reproductive events (i.e. from different zygotes, thus being different genets), derived from the binomial expression, is: This procedure can be used if the distribution of genetic distances among sampling units does not follow a strict unimodal distribution but shows high peaks toward low distances, susceptible to reveal the existence of somatic mutations or scoring errors in the data set resulting in low distances among slightly distinct MLG actually deriving from a single reproductive event. The use of the fre- quency distribution of distances to detect such events
When the same genotype is detected n times ina sample of N sampling units, the probability that the repeated genotypes originate from distinct sexual reproductive events (i.e. from different zygotes, thus being different genets), derived from the binomial expression, is: This procedure can be used if the distribution of genetic distances among sampling units does not follow a strict unimodal distribution but shows high peaks toward low distances, susceptible to reveal the existence of somatic mutations or scoring errors in the data set resulting in low distances among slightly distinct MLG actually deriving from a single reproductive event. The use of the fre- quency distribution of distances to detect such events
Fig. B1.2
Fig. B1.2
Table 1 Sampling geometries, strategies, and statistics used for clonal plants in 246 reviewed articles. The symbols are linking this infor. mation to the text and to the raw data available in Table S1, Supplementary material, detailing the findings of the literature review. The per centage of studies using various sampling geometries (shape of the area sampled) and sampling strategies (choice of sampling units) i: detailed; the frequency of the statistics used to describe clonal richness and diversity, as well as to ascertain clonal identity of the replicate: of the same MLG are also detailed. Finally, recommendations are suggested as to the use of sampling geometries, strategies and the choice of statistics (labelled * and ** corresponds to recommended and highly recommended methods, respectively) tif low perimeter /area ratio, note that squares and circles are inducing less edge effect. {If based on pilot studies or prior knowledge of average clonal size. §If not detrimental to the population. {Minimize the bias when N is low (lower than 20). ttIf necessary for comparison purposes. ttThe less redundant with classical richness estimates. §§Is the probability of getting a given MLGi when analyzing only one sampling unit, without taking into account the number of sam units, N, collected and analyzed. {Delivers the probability of getting n times a given MLG when analyzing exactly n and not N (sample size) sampling units. +ttAn average value is not reliable as the probability may be extremely distinct among genotypes, besides, this method does not tak account the number of sampling units analyzed.
Table 1 Sampling geometries, strategies, and statistics used for clonal plants in 246 reviewed articles. The symbols are linking this infor. mation to the text and to the raw data available in Table S1, Supplementary material, detailing the findings of the literature review. The per centage of studies using various sampling geometries (shape of the area sampled) and sampling strategies (choice of sampling units) i: detailed; the frequency of the statistics used to describe clonal richness and diversity, as well as to ascertain clonal identity of the replicate: of the same MLG are also detailed. Finally, recommendations are suggested as to the use of sampling geometries, strategies and the choice of statistics (labelled * and ** corresponds to recommended and highly recommended methods, respectively) tif low perimeter /area ratio, note that squares and circles are inducing less edge effect. {If based on pilot studies or prior knowledge of average clonal size. §If not detrimental to the population. {Minimize the bias when N is low (lower than 20). ttIf necessary for comparison purposes. ttThe less redundant with classical richness estimates. §§Is the probability of getting a given MLGi when analyzing only one sampling unit, without taking into account the number of sam units, N, collected and analyzed. {Delivers the probability of getting n times a given MLG when analyzing exactly n and not N (sample size) sampling units. +ttAn average value is not reliable as the probability may be extremely distinct among genotypes, besides, this method does not tak account the number of sampling units analyzed.
Table 2 Range of values reported for the main indices of clonal diversity and clonal size (linear) or surface area encompassed in different categories of clonal organisms (values for each study are detailed in Table S1)
Table 2 Range of values reported for the main indices of clonal diversity and clonal size (linear) or surface area encompassed in different categories of clonal organisms (values for each study are detailed in Table S1)
The distribution of elements into size classes has been shown to follow a power law for a very broad diversity of systems and phenomena, all of which (from dis- tributions in social sciences to astrophysics and the commonality of gene expression) conform to a parti- cular probability density distribution referred to as the Pareto distribution (e.g. Pareto 1897 in Vidondo et al. 1997; Ueda et al. 2004). A power law distribution applies to systems where the distribution of elements into classes is highly skewed, with much fewer large classes than small ones. The use of a power distribution allows the efficient and parsimonious description of the distri- bution of the studied elements into classes. We therefore propose here the use of the Pareto distribution as a con- tinuous approximation to describe the discrete distribution of sample units, or ramets (elements) into groups of clonal sizes (classes), where clonal sizes are defined by the number of sampling units belonging to that clone (MLL). This relationship is described by the equation: may be more appropriate than the calculation of a compound index. An overview of the literature shows that the distri- bution of replicates among lineages, when detailed, is always left skewed (all of the 45 studies reporting this information) with an exponential decay (Table S1). Transformed in a reverse cumulative frequency distribution, this empirical distribution can be approximated by a power law distribution, appropriately described by the Pareto distribution (e.g. Pareto 1897 in Vidondo et al. 1997; Box 4). All of the distributions of clonal membership found in the literature review conformed to the Pareto. This distribution indeed applied to a range of clonal organisms encompassing herbaceous plants and trees (Parks & Werth 1993; Hangelbroek et al. 2002; Chung et al. 2004; Nagamitsu et al. 2004), corals (Bastidas et al. 2001; Le Goff-Vitry et al. 2004), bivalves (Taylor & Foighil 2000), and ostracods (Cywinska & Hebert 2002). The model was shown to appropriately fit all of the distributions, with all x dependent on that of the heterogeneity indices they are based upon: if based on the Shannon-Wiener index, they will give more weight to the rarer components (species or genotypes) than when based on the Simpson index. n addition, a review of these and other evenness indices (Smith & Wilson 1996) reports that V’H “(= J’, equation 27) remains sensitive to changes in richness (also shown here below) despite intended to be independent of richness. As for richness and diversity, Simpson evenness values encompass the maximum, or almost the maximum, range (Table 2). Fig. B4.1: (a) Distribution of replicates among MLLs in Cymodocea nodosa from Alfacs Bay (Alberto et al. 2005), showing the steep decline in number of MLLs with increasing clonal membership typical of power law distributions; (b) transformed into a log-log reverse cumulative distribution.
The distribution of elements into size classes has been shown to follow a power law for a very broad diversity of systems and phenomena, all of which (from dis- tributions in social sciences to astrophysics and the commonality of gene expression) conform to a parti- cular probability density distribution referred to as the Pareto distribution (e.g. Pareto 1897 in Vidondo et al. 1997; Ueda et al. 2004). A power law distribution applies to systems where the distribution of elements into classes is highly skewed, with much fewer large classes than small ones. The use of a power distribution allows the efficient and parsimonious description of the distri- bution of the studied elements into classes. We therefore propose here the use of the Pareto distribution as a con- tinuous approximation to describe the discrete distribution of sample units, or ramets (elements) into groups of clonal sizes (classes), where clonal sizes are defined by the number of sampling units belonging to that clone (MLL). This relationship is described by the equation: may be more appropriate than the calculation of a compound index. An overview of the literature shows that the distri- bution of replicates among lineages, when detailed, is always left skewed (all of the 45 studies reporting this information) with an exponential decay (Table S1). Transformed in a reverse cumulative frequency distribution, this empirical distribution can be approximated by a power law distribution, appropriately described by the Pareto distribution (e.g. Pareto 1897 in Vidondo et al. 1997; Box 4). All of the distributions of clonal membership found in the literature review conformed to the Pareto. This distribution indeed applied to a range of clonal organisms encompassing herbaceous plants and trees (Parks & Werth 1993; Hangelbroek et al. 2002; Chung et al. 2004; Nagamitsu et al. 2004), corals (Bastidas et al. 2001; Le Goff-Vitry et al. 2004), bivalves (Taylor & Foighil 2000), and ostracods (Cywinska & Hebert 2002). The model was shown to appropriately fit all of the distributions, with all x dependent on that of the heterogeneity indices they are based upon: if based on the Shannon-Wiener index, they will give more weight to the rarer components (species or genotypes) than when based on the Simpson index. n addition, a review of these and other evenness indices (Smith & Wilson 1996) reports that V’H “(= J’, equation 27) remains sensitive to changes in richness (also shown here below) despite intended to be independent of richness. As for richness and diversity, Simpson evenness values encompass the maximum, or almost the maximum, range (Table 2). Fig. B4.1: (a) Distribution of replicates among MLLs in Cymodocea nodosa from Alfacs Bay (Alberto et al. 2005), showing the steep decline in number of MLLs with increasing clonal membership typical of power law distributions; (b) transformed into a log-log reverse cumulative distribution.
Fig. 2 Pareto plots showing the distribution of clonal membership across a range of species of terrestrial plants (Chung et al. 2004; Nagamitsu et al. 2004) and marine invertebrates: corals (Bastidas et al. 2001; Le Goff-Vitry et al. 2004), clams (Taylor & Foighil 2000) and ostracods (Cywinska & Hebert 2002). Pareto plots represent the fraction of sampling units belonging to clones representing by = X units as a function of X on a double logarithmic scale (Y = proportion of sampling units belonging to clonal lineages represented in the samples by X or more sampling units, and X = observed clonal sizes quantified as the numbers of sampling units found for every clonal lineage). This plot should display a straight line if the distribution of clonal membership conforms to a Pareto distribution, and the Pareto parameters can be estimated from the least squares regression line. The coefficient B, describing the Pareto distribution (-1 x regression slope), the correlation coefficient (r2) and the significance of the regression (P value) are given for each panel.
Fig. 2 Pareto plots showing the distribution of clonal membership across a range of species of terrestrial plants (Chung et al. 2004; Nagamitsu et al. 2004) and marine invertebrates: corals (Bastidas et al. 2001; Le Goff-Vitry et al. 2004), clams (Taylor & Foighil 2000) and ostracods (Cywinska & Hebert 2002). Pareto plots represent the fraction of sampling units belonging to clones representing by = X units as a function of X on a double logarithmic scale (Y = proportion of sampling units belonging to clonal lineages represented in the samples by X or more sampling units, and X = observed clonal sizes quantified as the numbers of sampling units found for every clonal lineage). This plot should display a straight line if the distribution of clonal membership conforms to a Pareto distribution, and the Pareto parameters can be estimated from the least squares regression line. The coefficient B, describing the Pareto distribution (-1 x regression slope), the correlation coefficient (r2) and the significance of the regression (P value) are given for each panel.
Fig. 3 The relationship between the parameters describing the Pareto distribution, and the richness and evenness level in the samples analysed. The data were obtained on the basis of simulations by distributing replicates (N = 50) among groups of genotypes (G = 5, 15, 25, 30, 45) across an increasing level of evenness (E = 1-5). The right panel illustrates the exponential increase of the Pareto parameter B with the level of evenness (72 between 0.60 and 0.93) for the five levels of richness explored. The left panel shows the exponential decrease in the size of the smallest size of genotype groups (in terms of number of replicates) with the increase in richness (r? between 0.91 and 0.99) for the five levels of evenness used.
Fig. 3 The relationship between the parameters describing the Pareto distribution, and the richness and evenness level in the samples analysed. The data were obtained on the basis of simulations by distributing replicates (N = 50) among groups of genotypes (G = 5, 15, 25, 30, 45) across an increasing level of evenness (E = 1-5). The right panel illustrates the exponential increase of the Pareto parameter B with the level of evenness (72 between 0.60 and 0.93) for the five levels of richness explored. The left panel shows the exponential decrease in the size of the smallest size of genotype groups (in terms of number of replicates) with the increase in richness (r? between 0.91 and 0.99) for the five levels of evenness used.
Fig. 4 Pareto plot of clonal membership distribution in four populations of the seagrass Posidonia oceanica (Es Castel, Porto Colom, Campomanes, Playa Cavallets). The coefficient 8, describing the Pareto distribution, the correlation coefficient (r2) and the significance of the regression (P value) are given for each panel.
Fig. 4 Pareto plot of clonal membership distribution in four populations of the seagrass Posidonia oceanica (Es Castel, Porto Colom, Campomanes, Playa Cavallets). The coefficient 8, describing the Pareto distribution, the correlation coefficient (r2) and the significance of the regression (P value) are given for each panel.
Fig.5 Cluster analysis of indices describing clonal diversity obtained on the basis of simulated data, using ‘1-Pearson 1’ as clustering distance: clonal richness R, Shannon-Wiener’s hetero- geneity H’ and Pielou evenness V’H’, Simpson’s complement heterogeneity D and evenness VD, and Pareto’s §. The same correlation and cluster structure was obtained on the basis of the Posidonia oceanica data set, with r values quantitatively similar to those obtained on the basis of simulations.
Fig.5 Cluster analysis of indices describing clonal diversity obtained on the basis of simulated data, using ‘1-Pearson 1’ as clustering distance: clonal richness R, Shannon-Wiener’s hetero- geneity H’ and Pielou evenness V’H’, Simpson’s complement heterogeneity D and evenness VD, and Pareto’s §. The same correlation and cluster structure was obtained on the basis of the Posidonia oceanica data set, with r values quantitatively similar to those obtained on the basis of simulations.
Fig. 6 (a) The relationship between the indices of clonal richness G and R and the number of sampling units N based on data sets of Posidonia oceanica (N = 149) and Cymodocea nodosa (N = 220), illustrating the absence of an asymptotic value of R and its strong dependence on sampling density. (b) Spline fit describing the rate of change in R with increasing N (OR/ON) for both samples (P. oceanica: = 1000; r2 = 0.21, P <0.05; C. nodosa: 0 = 1000; 12 = 0.78, P < 0.001).
Fig. 6 (a) The relationship between the indices of clonal richness G and R and the number of sampling units N based on data sets of Posidonia oceanica (N = 149) and Cymodocea nodosa (N = 220), illustrating the absence of an asymptotic value of R and its strong dependence on sampling density. (b) Spline fit describing the rate of change in R with increasing N (OR/ON) for both samples (P. oceanica: = 1000; r2 = 0.21, P <0.05; C. nodosa: 0 = 1000; 12 = 0.78, P < 0.001).
Fig. 7 Spatial autocorrelation analysis of Cymodocea nodosa in Alfacs Bay (from Alberto et al. 2005). (a) Clonal structure and subrange (on top). Kinship estimates from all ramet pairs or only for pairs between ramets showing a different multilocus genotype, and probability of clonal identity (proportion of pairs between ramets with identical multilocus genotypes), with confidence limits (for P = 0.975 and P = 0.025) based on 1000 permutations of spatial coordinates. (b) Genet level analysis (below), using a single copy for each multilocus genotype. The slope of the regression of mean kinship estimates as a function of the logarithm of spatial distance is plotted on the left, using as spatial coordinates the central zone occupied by multiramet genets, with broken lines delimiting 95% confidence limits around the null hypothesis of random distribution of genets in space. On the right side a single ramet per multiramet genet was randomly selected to create a 100-genet data file to generate the confidence limits for the correlogram.
Fig. 7 Spatial autocorrelation analysis of Cymodocea nodosa in Alfacs Bay (from Alberto et al. 2005). (a) Clonal structure and subrange (on top). Kinship estimates from all ramet pairs or only for pairs between ramets showing a different multilocus genotype, and probability of clonal identity (proportion of pairs between ramets with identical multilocus genotypes), with confidence limits (for P = 0.975 and P = 0.025) based on 1000 permutations of spatial coordinates. (b) Genet level analysis (below), using a single copy for each multilocus genotype. The slope of the regression of mean kinship estimates as a function of the logarithm of spatial distance is plotted on the left, using as spatial coordinates the central zone occupied by multiramet genets, with broken lines delimiting 95% confidence limits around the null hypothesis of random distribution of genets in space. On the right side a single ramet per multiramet genet was randomly selected to create a 100-genet data file to generate the confidence limits for the correlogram.
*available in the newly released version of GENCLONE, GENCLONE 2.0. Data sets analysed, methods to assess clonality and clonal membership, clonal diversity estimates, and methods proposed tc describe spatial components of clonal growth: GENALEX (Peakall & Smouse 2006), GENCLONE (Arnaud-Haond & Belkhir 2007) GENOTYPE and GENODIVE (Meirmans & Van Tienderen 2004) and MicsiIm (Stenberg et al. 2003).
*available in the newly released version of GENCLONE, GENCLONE 2.0. Data sets analysed, methods to assess clonality and clonal membership, clonal diversity estimates, and methods proposed tc describe spatial components of clonal growth: GENALEX (Peakall & Smouse 2006), GENCLONE (Arnaud-Haond & Belkhir 2007) GENOTYPE and GENODIVE (Meirmans & Van Tienderen 2004) and MicsiIm (Stenberg et al. 2003).
Related topics:
GeneticsSpatial autocorrelationSoftwareBiological markers
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved