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A Foliar Morphometric Approach to the Study of Salicaceae.

I. Abstract

An assemblage of leaves of four species of willows (Salix viminalis, S. alba, S. fragilis, and S. caprea), two of their hybrids (S. alba x fragilis and S. caprea x viminalis), two species of poplars (Populus alba and P. tremula) , and two "external" species (Elaea gnus angustifolia and Pyrus salicifolia) was analyzed. The study was designed to determine whether leaves that are very close in shape but belong to different species, particularly the elongated leaves of S. viminalis, S. alba, S. fragilis, E. angustifolia, and P. salicifolia, could be discriminated by continuous foliar characters (that is, vegetative characters), despite both the great foliar polymorphism met in Salicaceae (especially in the genus Populus) and hybridization problems. Our results show that multivariate analyses (principal component analysis [PCA] and cluster analysis) of an appropriate character set enable leaves to be classified in their own species at more than 98%, even in these difficult conditions. It can be seen from this wor k that PCA is a good tool when it keeps a maximum of total variability; that is, when there are few taxa; on the other hand, cluster analysis is more appropriate with many taxa. One can then envisage the application of this morphometric approach to fossil-imprint determination, in which even fragmentary paleobotanical remains could be included. This would give access to real biodiversity of tertiary flora and to intraspecific variability.

II. Introduction

The search for evolutionary lineage has long been based on qualitative evaluations of morphological change, resting on empirical appreciation of form. Thus, during the nineteenth century, in Cenozoic paleobotany, researchers tried to find the closest extant genus or family to the studied imprint. Foliar polymorphism was rarely taken into account, and several determinations were or are still imprecise. With the arrival of the biological species concept, systematic studies were no longer interested in a morphologically unchanging type; attention turned to a community of individuals that were more or less different from one another. This new approach required the use of quantitative statistical methods, in order to access the variability of samples representative of populations.

The subject of morphometrics, according to Rohlf(1990, in Yoccoz, 1993), is quantitative description, analysis, and interpretation of size and form variations observed in a living being. Most of the time these same morphological features support empirical approaches to systematics; that is, naturalistic perceptions of life. Morphometrics must be complementary to these perceptions, bringing out nonvisible information and obtaining comparable results. This is not numerical taxonomy: The aim is not to rediscover or create a classification but to establish links between specimens using different statistical techniques, including cluster analysis.

In the study of paleogene macroflora, the number of features is limited: Vegetative and reproductive organs are almost always dissociated; color, texture, and volume are absent; and there is diverse damage and artifacts. Therefore, only well-preserved material, with visible venation and/or organic matter, allows accurate specific determinations. Thus, many fragmentary fossils were neglected during interpretation of this ancient floral biodiversity.

In Cenozoic paleobotany, morphometric methods can only be applied to the most common material: foliar imprints. This work therefore aims to evaluate the efficiency of a morphometric approach in determining extant leaves first, in order to then determine fossil-leaf imprints. Clustering of well-preserved and identified foliar imprints, and fragmentary ones, according to their taxon, would in fact allow the determination of these incomplete remains. If this technique can be used to identify even the fossils that lack the features necessary for their determination, then they could be included in paleobotanical studies, in order to understand the real biodiversity of tertiary flora and specific variability.

In 1980, Hill proposed a set of continuous characters, inspired by Blackburn (1978) and Stace (1965), to be used for statistical tests on Angiosperm leaves and obtained 100% positive results with 20 extant species using cluster analysis. His work on missing data, number of characters, sample size, and character correlation seemed to support the use of morphometrics in paleobotany. In an earlier study (1998) I was able to show that 15 foliar characters submitted to different uni- and multivariate analyses enabled the discrimination of both extant and fossil species of the genus Salix even though all of these species have very similar leaf-blade forms.

The family Salicaceae is particularly interesting because its phylogenetic affinities are not yet well known, and it contains two genera whose evolution was quite different and exhibit both very advanced and primitive features. It is also a family that unites all potential difficulties for such a study: Hybrids are very frequent in Salix, and there is great foliar polymorphism in both of the genera, Salix and Populus. Furthermore, there is a problem specific to Salix: its great foliar similarity to species of Lauraceae, from which it cannot be differentiated without certain venation characters. The genus Salix therefore illustrates a frequent tertiary paleobotanical problem due to its resemblance to Lauraceae: quantification of the respective parts of temperate and tropical species in Cenozoic flora, and the paleoecological consequences.

The study of several foliar characters of extant material in four willow species, some of their hybrids, two species of poplars, and two other species close in foliar morphology to the species of Salix studied should allow us to test the efficiency of this set of characters in clustering each leaf in its species by multivariate analyses (because specimens are extant, determinations are carried out beforehand), to evaluate the relative utility of the different measured characters according to their correlations and environmental plasticity, to visualize the "morphological space" of taxa and their hybrids within extant Salicaceae, and the limits of this space between taxa of the same species/genus/family, and, finally, to determine whether, under certain conditions, morphometrics are useful tools in Angiosperm systematics and paleobotany.

III. Materials and Methods

All of the studied specimens came from the Herbarium of Claude Bernard University, Lyon 1, (Herbier Chassagne, Rouy and Baetniz, reviewed by Chassagne), except Elaeagnus leaves, which were collected in the field. Subspecific determinations within the genus Salix are nonsense because this genus constantly evolves with hybrids in different generations. The studied material consisted of:

1. Four species of Salix (Salicaceae): S. alba, S. fragilis, and S. viminalis, with a lanceolate-linear characteristic form of the blade and acuminate apex; and S. caprea, with a rounded elliptic form of the blade, obtuse apex.

2. Two hybrids of Salix: S. alba x S. fragilis and S. caprea x S. viminalis.

3. Two species of Populus (Salicaceae): P. alba and P. tremula, whose blades are more rounded and similar to S. caprea. Among the broad polymorphism in these two species of Populus, two characteristic forms are distinguished for each species, leaves from both long and short twigs, with all intermediates existing in nature.

4. Two "external" species chosen for their elongated form of blade, similar to that of S. viminalis, S. alba, and S. fragilis; namely, Pyrus salicifolia (Rosaceae) and Elaeagnus angustifolia (Elaeagnaceae).

Only 10 specimens of each species were studied, because we wanted to create the same conditions as when we study fossil material, where few well-preserved imprints are available and fragmentary imprints can be added later for determination purposes.

Our sample was made up of all of these leaves. According to Dorf (l969), between 500 and 1,000 specimens per sample are required per outcrop to obtain correct determinations for fossil leaves. In contrast, Dolph (1976) found that increasing sample size only brings more confusion to the classification. Finally, Hill (1980) showed that if the character set has enough discriminatory power, sample size is not important. The choice of 10 specimens per species seemed sufficient, for Hill obtained a 100% correct classification with only five specimens. From my previous results (1998) it also appears that a few specimens are enough to obtain correct classification, as long as all taxa are evenly distributed. The 10 leaves studied were chosen for their good conservation, from base until apex of a vegetative twig, on several herbarium loans, to keep as much phenotypic variability as possible, despite great intraspecific variability.

Each distance was measured with a digital calliper rule. This ensured the quality of the reading and sped up the measuring. Angles were measured using a protractor, and a leaf-form index, i, was determined with a grid drawn on a transparency. A low-power stereo microscope was used for small angles and distances.

A. CHARACTER SET

According to Sneath and Sokal (1973), at least 60 variables are required to obtain good results in morphometrics. However, such a quantity of characters is difficult to achieve with angiosperm leaves. With 31 characters, Hill (1980) obtained 100% correct results; and with only 14 characters (that is, without cuticular or tertiary venation characters, which are scarcely observable in fossil leaves) he found no more than 3% misidentified specimens.

We used some of Hill's characters (the 14 that are observable with fossil imprints) and others suggested by Blackburn's (1978) morphological variables and Stace's (1965) stomatal characters because they seemed well adapted to our study. Hill's variables in fact have great discriminatory power and thus imply that sample size is less important and are very useful in view of the correlation between characters and missing data (Hill, 1980). Some new characters were added that are available in the present material and that were missing in my previous study (1998). This study was based on 26 measures, which could be combined in several proportions and ratios between characters, thus leading to a possible 100 variables.

All of these characters are continuous variables. Although such characters take longer to score, more powerful statistical tests can be applied to them unlike the case with simple binary characters. Moreover, they allow an objectivity that is impossible with binary characters.

The following is a list of the characters used and illustrated in Figure 1:

1. Leaf length, L, from apical extremity to petiole insertion point, along the primary vein, in millimeters (Fig. 1a). This can be expressed as a ratio to several characters.

2. Leaf width, 1, maximal width of the leaf measured perpendicular to the primary vein in millimeters (Fig. la). This can be expressed as a ratio to several characters.

3. Leaf-form index, i, shown in Fig. 1b and defined by Hill (1980) as: "A circular grid with lines marked at set angles... placed over the leaf so that the 90[degrees]-270[degrees] axis lies at the maximum width of the leaf and the origin lies over the primary vein. The perpendicular distance from the primary vein to the intercept of each line with the margin is measured, giving 36 measurements" (i = 200 M/I).

4. Position of 20% maximum width basally, 20%b, the distance in millimeters from the base to the position of 20% maximum width basally (Fig. 1a). This can be expressed as percentage of the leaf length, L, and as a ratio to b[degrees], b-l, and other characters.

5. Position of 20% maximum width apically, 20%a, the distance in millimeters from the apex to the position of 20% maximum width apically (Fig. 1 a). This can be expressed as percentage of the leaf length, L, and as a ratio to a[degrees] and other characters.

6. Base angle, b[degrees], the angle in degrees between the lines joining the intersections with the margin of 20% maximum width basally and the base (Fig. 1a).

7. Apex angle, a[degrees], the angle in degrees between the lines joining the intersection with the margin of 20% maximum width apically and the apex (Fig. 1a).

8. Petiole length, p, in millimeters (Fig. la). This can be expressed as a ratio to leaf length, L, b-l, and so forth.

9. Position of maximum width, b-l, the distance from the base to the maximum width, measured along the primary vein in millimeters (Fig. 1 a).

10. Number of secondary veins, nII, the mean of the number of secondary veins counted for both sides of the primary veins. This can be expressed as a ratio to L, xy, wx, and so forth.

11. Secondary vein length, xy, measured on each side of the primary vein, on the four secondary veins closest to the maximum width, I (Fig. 1 c). This can be averaged, studied by pairs, compared with respect to the position of the vein where it was taken, and so forth.

12. Distance between secondary veins, wx, measured on each side of the primary vein, between the four secondary veins closest to the maximum width, 1 (Fig. 1 c). This can be averaged, studied by pairs, compared with respect to the position of the vein where it was taken, and so forth.

13. Secondary-vein emergence angle, IIa[degrees], the angle in degrees between the primary vein and the tangent to point a, located on the adaxial 10% length of the secondary vein, 10% xy (Fig. 1c) and measured on the four secondary veins closest to the maximum width, 1 (high curvature often occurs in the first 10% of the secondary vein at the junction with the primary vein). This can be averaged, studied by pairs, compared with respect to the position of the vein where it was taken, and so forth; and it can be compared with II[degrees]b, II[degrees]c, xy, wx, nII, and so forth.

14. Basal-secondary-veins emergence angle, II[degrees]ab, the angle in degrees between the primary vein and the tangent to point a, located on the adaxial 10% length of the two basal secondary veins, 10% xy. This can be compared with II[degrees]a, b[degrees], and so forth.

15. Secondary-vein margin angle, IIb[degrees] the angle in degrees between the primary vein and the line joining the abaxial end of a secondary vein to the position of the 10% adaxial length, a, measured on the four secondary veins closest to the maximum width, 1 (Fig. 1c). This can be averaged, studied by pairs, compared with respect to the position of the vein where it was taken, and so forth; and it can be compared with II[degrees]a, II[degrees]c, xy, wx, nII, and so forth.

16. Secondary-vein straightness index, II[degrees]c, the length in millimeters of the secondary vein between the midrib and the point where the tangent to the secondary vein first makes an angle of 200 with the tangent to the position of the adaxial 10% length of the secondary vein. This can then be expressed as a percentage of the total length of the secondary vein and is averaged for the four secondary veins closest to the maximum width, 1. It can be averaged, studied by pairs, compared with respect to the position of the vein where it was taken, and so forth; and it can be compared with II[degrees]a, II[degrees]b, xy, wx, nII, and so forth.

17. Number of intersecondary veins, ninterII, the mean of the number of intersecondary veins counted on each side of the midrib. This can be expressed as a percentage of the number of secondary veins, nil, and as a ratio to wx, II[degrees]a, and so forth.

18. Number of teeth along the whole leaf, nD, the mean of the number of teeth counted on each margin. This can be expressed as a ratio to L, nII, and so forth.

19. Number of teeth at the apex, nDa, the mean of the number of teeth counted on each margin 1 centimeter from the apex. This can be compared with nD, 20%a, i, a[degrees], and so forth.

20. Number of teeth at the base, nDb, the mean of the number of teeth counted on each margin 1 centimeter from the base. This can be compared with nD, 20%b, b[degrees], b-l, and so forth.

21. Number of teeth at the maximum width, nD1, the mean of the number of teeth counted on each margin 1 centimeter from the point of maximum width. This can be compared with nD, 1, i, b-1, and so forth.

22. Apex curvature angle, the angle in degrees between the axis of the primary vein at the base and the axis of the primary vein at the apex of the leaf.

All of the characters used are elements of the blade and concern leaf size, form, and venation. This diversity will certainly allow us to better face variations in size (due to environment or age) and form (due to foliar ontogeny, for example). Ultimate venation and the stomatal complex, which are very useful for extant angiosperm leaf determinations, were not used here because they are scarcely observable on fossil material. The goal of this work is precisely to see whether it is possible to identify the countless quantities of less well preserved or fragmentary leaves from tertiary paleoflora. Thus this character set is made up of angles, distances, and ratios.

Because venation of the leaves studied here is quite simple, we used Mouton's (1967) definition of venation types: that the primary vein is made up of all of the veins that come directly from the petiole, that the secondary venation consists of all of the largest veins connected to the midrib, and that the tertiary venation is linked to the secondary venation. These characters only concern foliar morphology, and they are all vegetative. This avoids any confusion in these groups based on reproductive characters because males cluster together, rather than with their female counterparts (Crovello, 1968).

B. DATA TRANSFORMATION

Usually, because each data set is made up of gross distances, it is necessary to reduce size differences by dividing values by the measure that best expresses individual variations in size. In this way, differences in form show up. This avoids the discrimination of specimens depending only on their size, which is highly influenced by environment, growth rates, and other variables. From a theoretical point of view, indexes were criticized because of their non-objectivity and because their distribution is often asymmetrical, with significant deviations from a normal distribution (Ambroise & Geyssant, 1974). It is better to avoid a priori use of ratios because of autocorrelation between variables (Yoccoz, 1993). Other techniques have been proposed, such as the transformation of characters into standardized variables or the use of the first PCA factor as a divisor.

In the present study, the character set contains not only gross distances but also angles and indexes. It therefore makes no sense to divide by a size measure (L, if we had to choose one). Because certain variables are directly linked to blade form, it does not seem necessary to carry out any a priori gross value weighting. On the other hand, we will try to standardize characters according to Blackburn's (1978) method in order to avoid having those with the greatest variance contribute most to classification. With this technique, all variables will be divided by a number, k, of equal-sized states ranging from 1 (for the state containing the lowest values) to k (for the kth state, containing the highest values): k 1 + 3.332 log n, where n is the total number of leaves in the sample. This method is not greatly affected by outlying values from character sets (Hill, 1980).

C. DATA PROCESSING

Data processing was carried out using UNISTAT Statistical Package (UNISTAT, 1995) which is powerful and quite easy to use. The Shapiro-Wilk test of normality is a powerful alternative to one-sample Kolmogorov-Smimov test against normal distribution when specimens number fewer than 50. Kendall's robust nonparametric rank correlation, statistical tests (F, t, and nonparametric Mann-Whitney U-tests), and multivariate analyses (PGA, hierarchical cluster analysis with centroid squared euclid distance, and canonical discriminant analysis) were applied.

IV. Results

With very rare exceptions, all characters follow a normal distribution. The samples are, therefore, representative of homogenous populations. The study of correlation coefficients and of character distribution for all extant species according to PCA axes highlights interesting and sometimes surprising information. For example, one can observe which characters are correlated with leaf size, see links between size and form, and so forth (Fig. 2). Leaf size is correlated with almost all other variables, because of both environmental and ontogenic variability, and this can be corrected by dividing their value by L, 1, or L/1. However, some variables are completely independent of leaf size. These include secondary venation, dentation, and certain leaf-form characters. These characters have generally good and sometimes excellent discriminatory power.

Intraspecific variable characters differ from one taxon to another. Nevertheless, some general observations can be made from the correlations among all taxa: secondary veins constitute the width of the leaf, 1, which, combined with leaf length, L, make the leaf form. L is, however, mainly due to epigenetic factors (light, temperature, and rainfall) while I proves to be the major limb-form character. The longer the leaf, the narrower it is; the longer the apex, the more secondaries and intersecondaries there are; the farther the maximum width is from the base, the more acute the extremities are; and the more curved and spaced the secondaries are, the shorter the petiole is (Fig. 2). The apex and base are correlated with each other because of their important link to leaf form, but they do have different properties. The apex is closely linked to secondary venation, and its shape is particularly important for water movement and may be determined by venation. The form and venation of the base are usually quite in dependent of other variables. Length and distance between base secondaries are influenced by leaf length, L. When the leaf is curved, the angles of the secondaries differ from one side of the primary to the other. The angles of the secondaries, II[degrees]a and II[degrees]b, are more obtuse, and the teeth are less numerous. The number of teeth is independent of leaf size and shape.

It is not superfluous to create a new character from the ratio of two variables because often these characters are not correlated with the ratio, and they can be very efficient for discrimination. Ratios that are almost always used are xy/wx, L/1, p/L; (b-1) x 100/L, b[degrees]/20%b, and nII/xy. The ratio of petiole length to leaf length or to the number of secondaries is a constant.

The study of Salix alba, S. fragilis, and S. alba x S. fragilis illustrates the problems posed by the differentiation between two species with very close leaf forms and their hybrid. Salix alba and S. fragilis are clearly separated by PCA shown in Figure 3, in which the vertical axis represents intraspecific variability and the horizontal axis represents interspecific variability. These two species are differentiated by the angle of the secondary veins and leaf form, with the leaves of S. alba being elongated, smaller, with a more acute apex, fewer, more acutely oriented secondaries, a shorter petiole, and more numerous teeth at maximum leaf width than the leaves of S. fragilis. Cluster analysis distinguishes the two species, but one leaf, that of S. fragilis, is almost always isolated in the dendrogram, depending on the character set used. When the hybrid S. alba x S. fragilis is added, irrespective of the character set used, with both cluster analysis and PCA S. alba and the hybrid are mixed.

The case of S. caprea, S. viminalis, and S. caprea x S. viminalis is interesting. It demonstrates how two species with very different leaf forms can be separated and how they divide their characters between their hybrids. S. caprea and S. viminalis are distinguished perfectly by both PCA and cluster analysis. Even two "varieties" or "forms" of S. caprea are separated by cluster analysis. The two species are differentiated by characters of leaf form, and also by secondary venation. With only form variables, the classification obtained by cluster analysis is perfect; but, in contrast with only venation variables, one leaf is badly classified, and, with only size variables, the leaves from both taxa are all mixed. From PCA it appears that S. viminalis has longer, curved, and narrower leaves, with more secondaries and intersecondaries, that its apex and base are more acute, and that its secondaries are oriented at a more acute angle and are closer to each other than are those features inS. caprea. PCA of these t wo species and their hybrid shows three well-isolated groups, corresponding to the three taxa (Fig. 4). The intraspecific variability (vertical axis) is linked to size characters. Cluster analysis once again gives some less-clear results. The hybrids share characters from both parents equally and are situated halfway between them, except for secondary venation.

When all four Salix species and their hybrids are studied together, PCA (Fig. 5) and cluster analysis segregate them perfectly, except for hybrid S. alba x S. fragilis, which is always nearer to S. alba. At the specific level, however, the results are perfect. Leaf-form characters are enough to separate S. caprea from S. viminalis and their hybrid. However, to separate S. alba and S.fragilis it is necessary to include the angle of the secondaries and teeth characters. These characters by themselves do not, however, allow discrimination between S. caprea and S. viminalis and their hybrid. The results are slightly better when the data are transformed following Blackburn's method, but S. alba x S. fragilis still groups with S. alba.

As with Salix, PCA clearly isolates every Populus alba from every P. tremula, but cluster analysis does not. Venation characters differentiate these two species, including short- and long-twig leaves; and, regardless of the great heterophylly found in both species, all leaves are correctly classified.

PCA of the entire sample-that is, combining the data all leaf samples of all taxa-gives very poor results: Salix alba, S.fragilis, and S. cap rea overlap each other, as do Populus alba and P. tremula. At the generic level the segregation is good, except for Eleagnus angustifolia, whose leaves are very close to those of the S. alba, S. fragilis, and S. caprea group. In the dendrogram, all species except P. alba and P. tremula are recognizable as isolated. If we add the characters that were noted as being especially good for discriminating of P. alba from P. tremula, PGA is better; and the dendrogram is almost perfect, with only one P. alba leaf clustered with P. tremula (Fig. 6). All of the elongated leaves are therefore correctly classified. Without the leaf-form index, i, the classification is less good, so despite the time needed to make this measurement, it seems necessary to keep it.

When all of the characters are ranked according to Blackburn's method, the results are much worse, so it is not worthwhile spending time to transform the data in that manner.

V. Discussion

Some astonishingly good results were obtained, in that each leaf, except for one leaf of Populus alba, was correctly classified in its species. The fact that Salix alba x S.fragilis and S. alba are always clustered is not a misclassification but, rather, indicates that these hybrids are very close to S. alba. Have they inherited more characters from S. alba, whose alleles could be dominant, or is it because the degree of affinity is greater for this species (second- or third-generation hybrids are very frequent in this genus)? A genetic study is required to know more about this. However, that the hybrid and S. alba are grouped together does not really matter much here, because such precise determinations are not required in studying fossils. In paleobotany, identifications are required even when there are no flowers or fruits. Morphometrics can therefore allow us to establish parallels and at least to say that it may be a hybrid, or that it is a close form of species X, and that a paleobotanical species is m orphologically close.

For the hybrid between Salix caprea and S. viminalis, the division of characters is different. The new combination has created different values of secondary venation angles, and all of the other characters are intermediate between the parents. This illustrates the possibility of obtaining new character combinations from one generation to the next and explains why Salix hybrids are often more vigorous and thus more numerous than are their parents.

An unexpected result was that the short- and long-twig leaves of Populus could be recognized as a same species. It would seem, from qualitative examination, that there is as much difference between short- and long-twig leaves in one species of Populus as there is between long-twig leaves of the two species of Populus. One of the powerful uses of this quantitative method is that it reveals some "invisible" characters that are useful for discriminating seemingly intractable identifications. Moreover, foliar polymorphism is not an obstacle to the use of morphometrics.

Morphometrics also allowed the establishment of correct classifications for an assemblage of polymorphic leaves of different species of Salix and their hybrids with very similar leaf forms, as well as some external species, such as Eleagnus angustifolia, whose leaves are very close in form to those of Salix. The success of this method in such an extreme case is encouraging for further applications, particularly in paleobotany, where leaves are almost always dissociated from the rest of the plant.

This work improved our knowledge of the studied species. In addition to qualitative characters found in the literature, it introduced new quantitative characters that are specific to each taxon. We can envisage a databank containing information about the morphology and cuticle of angiosperm leaves, as suggested by Dolph (1976), as well as some statistically testable continuous characters, such as those used here for each extant or fossil taxon in the database.

Multivariate analyses associated with a good continuous character set (inspired by Hill, 1980) allowed the correct and objective classification of98% of leaves of extant species present in the sample. This confirms Hill's conclusions that a reduced number of variables is enough to cluster taxa properly, even when they are strongly correlated (Hill, 1980). During my previous study (1998) I had to remove some size variables-L and b--l--from the character set that confused classification. Deleting the characters that were responsible for a large part of the total variability did not modify but improved discrimination. Here it was sometimes observed that, to obtain a good classification, size variables were not necessary but also that they never caused confusion. The number of characters used was much greater here than in my earlier study (1998), as were the number and the variability of taxa. Therefore, as many variables as possible must be kept. Some characters have more discriminatory power than others, but t hey differ according to taxon; and, although one variable may allow good discrimination between two species, it may be of no use for other taxa. Often blade form, margin and venation characters are the most discriminatory. The latter are subjected to little epigenetic variation and have a better chance of being characteristic of a particular species. This also emphasized by the fact that good discriminatory characters are often independent of each other. This explains why the use of ratios was very fruitful and not redundant in most cases. It has been shown that leaf length and apex vary according to moisture and temperature (Wilf, 1997), and it is true that these characters are never independent of some others. They are, however, often characteristic of intraspecific variability and, therefore, do not have good specific discriminatory power. The best-substantiated theories link moisture to leaf size and to the presence of drip-tips, which are attenuated, elongated leaf apices that appear to control the rate of water loss from the leaf surface (Wilf, 1997).

The fact that a variable is independent of others (and of leaf length) does not mean that it is independent of the environment. For example, many studies show that teeth are strongly associated with the movement of water out of leaves via transpiration and guttation. This suggests that one of the functions of teeth in colder climates is to boost sap flow and also that untoothed margins correlate with leaf thickness and, in turn, with temperature. The decreased flow resistance in thicker leaves thus allows more even growth between secondary veins, which results in a smoother margin (Wilf, 1997). Margins and secondary venation characters are not, therefore, free of epigenetic factors; but, compared with leaf length, apex, and so forth, they are influenced differently by the environment. That these characters are very discriminant could mean that they are determined by the environment at a specific level rather than at an individual level. However, here we are interested in including all variability factors--ge ographical, climatic, and ecological--in order to know whether the morphometric method is of real interest under as unrestrictive conditions as possible. Because morphometrics work under such difficult conditions, they are robust, as demonstrated here.

Character correlations are very complex and often governed by epigenetic factors. We have already discussed the behavior of leaf length, width, apex, base, venation, and margins. All of these links illustrate the balance that exists between blade structures that create a perfectly adapted organ in which all characters play an important role in the overall foliar architecture. These observations show the many perspectives resulting from this work. Of value would be further studies to better understand the correlations at the anatomical level, as well as studies of the growth and development of leaves along a twig.

When many taxa are studied it is necessary to use as many variables as possible, in order to obtain the best results. Therefore, when ultimate venation and stomatal characters are not available--as is often the case in paleobotany--blade form, margin features, and secondary venation characters are the most discriminant between species of the same or different genera. However, all of these variables are important, for each contributes to total variability. A character set such as that used here allows coherent groupings to be found among a set of leaves of different forms and phylogenetic origins. The choice of characters included in the set is very important for the methods of multivariate analyses to be successful. In this study, the set was made up of 22 basic characters and of 10-20 ratios of these.

Because my previous work was limited to elongated leaves, i and L/1 were very strongly correlated (1998). For this reason, in that study it did not seem useful to keep the leaf-form index, i, which requires 36 measurements to be taken on each leaf. In studies with different blade forms, such as the one presented here, if i is removed from the character set the results are worse and of less value.

The present study shows that all of the statistical techniques used are of some interest. The most sophisticated methods, such as cluster analysis, are more useful and allow better interpretations when they are accompanied by other, more classical techniques, such as PCA or comparison tests. Cluster analysis indicates the groups directly, whereas PCA provides a visual aspect of these group formations. PCA reflects each taxon's distinct morphological space, which, in turn, allows us to understand how--that is, according to which variables--these clusterings were achieved. This means that we can better define, qualify, and understand the groups. It also teaches us a great deal about the correlations between variables. Finally, PCA is the best method when there are few taxa and when a summary of the information given by all of the characters measured in all of the specimens is enough achieve the desired discrimination. When the number of taxa increases, the discriminatory characters for all of the species prese nt are different, and the characters vary considerably intraspecifically, then a summary of the information is no longer sufficient. Cluster analysis, which takes into account all of the information, then takes over. In the case of S. caprea, Salix viminalis, and S. caprea x S. viminalis, cluster analysis gave poorer results than did PCA. This shows that the PCA summarizes the information well (84% of variability is kept in this case). With only few taxa and with much variation between characters, a compromise is better. Comparison tests can provide information that is not shown by other techniques, because these tests enable each variable to be studied independently. Multivariate analyses synthesize information derived from all of the characters. This can be useful in certain cases, such as during my previous study (1998), when I was able, for example, to observe that the only character that differentiated S. viminalis, an extant species, from S. angusta, a fossil species, was petiole length. Blackburn's (19 78) method contributed nothing new in either my earlier study or the present one. When there were few taxa, the groups obtained by PCA were narrower, and when the whole sample was considered, the classification found following Blackburn's standardization was more confused and less useful.

The method presented here is reliable at the specific level but not always at the intraspecific level. We are not, however, looking for natural classifications; we want taxa to be isolated, not to be systematically classified. This method is not intended to study phylogeny directly, for this is very much based on the similarity of form of one organ, which is, furthermore, strongly affected by environment. This means that synapomorphies, plesiomorphies, autapomorphies, and homoplasies are used. However, a study by David and Laurin (1996) comparing morphometric and cladistic approaches revealed perfect congruence of the results between both methods. This implies that, in that study, morphometric characters were not homoplasious. However, it must be remembered that the leaf is an organ that is strongly affected by the environment and so is highly likely to follow parallel evolution and exhibit considerable homoplasy. Relationships between different species and genera are not, therefore, deductible from such den drograms, particularly for vicariant or convergent forms that can be artificially associated in morphometric analyses. In palaeontology interfertility criteria are unusable, and DNA sequencing is very controversial at best, so morphometrics is one of the only ways to reconstruct a supposed genealogical tree of each species by allowing at least the comparison of morphological spaces. This approach can lead us to a better understanding of the species concept in paleobotany.

From the excellent results obtained with extant material, it now seems possible to apply this method to fossil material. We have assemblages containing different species that we would like to discriminate--for example, elongated foliar-imprint assemblages containing both Salicaceae and Lauraceae. The method could then be used to discriminate any fossil species on the basis of foliar imprints or of other organs. The morphometric approach allows us to use a broader sample of remains, except for those that are really too damaged or poorly preserved. This, in turn, would lead to better assessment of real biodiversity, of intraspecific variability, of the relative frequency of different species in a fossil assemblages, and of the relative conditions of fossilization. The comparison of same-age outcrops would thus give access to geographical variability, and the comparison of successive levels would inform us about evolution modalities and rhythms that are correlated with climatic and topographic conditions. Two l evels of the same outcrop can contain very different material, according to their sedimentation modes--high or low energy deposits. The comparison of these levels can provide further information about taphocoenosis, dissemination, degradation, persistence of foliage, distribution of species, and the success of fossilization according to leaf buoyancy.

Using morphometric approaches, some relationships between climate and some foliar characters were shown. These include venation-network density (Manze, 1968; Dilcher, 1974); percentage of entire margined leaves as well as specific richness (Dolph, 1976); and leaf size and camptodromous and craspedodromous venation (Mouton, 1967). Comparisons between extant and fossil flora would lead to advances in paleoclimatology.

The ideal procedure for studying fossil material would be as follows: Take as many measurements as possible on a reduced sample of 100-150 determined specimens, chosen for their good conservation and representativeness of the total sample; use multivariate analyses to see which characters are the most discriminant and to delimit clusters equivalent to taxa in the dendrogram; and, based on these results, measure only the useful characters in all of the specimens. In this way we would save time during the second stage of the work, especially as we would already be accustomed to taking measurements and familiar with data treatment. At the end of this stage, every imprint would be assigned to a taxon, irrespective of whether it had been determined by morphological observation. If some leaves were still not classified, it would mean that either they were too badly preserved or that they represent a new taxon that was not recognized in the preliminary stage. It must nevertheless be borne in mind that, if a leaf is too badly preserved or damaged and lacks secondary venation, apex, and /or base, it will remain difficult to classify even by using statistical techniques. The total time spent determining each imprint will finally be reasonable. Not only will each leaf be determined, but objective and measurable characters that support the representation of each taxon will be identified and will allow us to make many comparisons--for example, between outcrops, levels, species, genera, families, and so forth.

In conclusion, the morphometric approach used with an appropriate character set led to the goal of accurately discriminating leaves at the genus, species, and even hybrid levels, despite great polymorphism and the similarity of blade form in certain species. The real utility of this method will, however, only be tested when it is applied to fossil material. A clear advantage of this technique is that it enables many comparisons to be made on the basis of continuous, objective characters. This opens the way to paleoecology, s.l., and to the comprehension of evolution modalities and of the species concept for fossil leaves. One must not, however, adopt a reductionist stance. A few foliar characters cannot summarize all of the information contained within an organism and its environment. Morphometrics remains a tool that is modern and efficient, but it must be integrated into the ensemble of methods that are already used--morphology, cuticular analysis, and palynology--as well as those that are still being deve loped, such as geometric morphometrics, fossil DNA sequencing, and outcrop comparison in cladistics.

VI. Acknowledgments

I wish to thank Mr. Barale and everyone in the laboratory of Biodiversite, Evolution des Vdgetaux actuels et fossiles, Lyon 1, who supported this research, as well as the participants, for advice and encouragement, in the Symposium Morphometries et Biologie Evolutive held in October 1998 and organized by the National Natural History Museum of Paris.

VII. Literature Cited

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Thiebaut, M. 1998. Determination d'empreintes foliaires fossiles d'angiospermes du gisement oligocene de Cereste (Alpes-de-Haute-Provence) a l'aide d'une methode morphometrique. Courrier scientifique du Parc naturel regional du Luberon 2: 20-31.

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Wilf, P. 1997. When are leaves good thermometers? A new case for leaf margin analysis. Paleobiology 23: 373-390.

Yoccoz, N. G. 1993. Morphometrie et analyses multidimensionnelles: Une revue des methodes separant taille et forme. Pp. 73-99 in M. Masson (ed.), Biometrie et environnement. Centre national de la recherche scientifique, Paris.
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