The most classic and straightforward applications of morphometric approaches are (i) the study of shape differentiation between extant or past populations or species (e.g. Dommergues et al., 2006 and Neige, 2003); and (ii) the quantification of shape disparity through time and/or geography (e.g. Dera et al., 2010, Lefebvre et al., 2006 and Moyne and Neige, 2007). This quantification is performed by studying the occupation of a multivariate space, called “morphospace” (for a review on theoretical morphospaces, see Dera et al., 2008), resulting from multivariate analyses on shape variables. For extant data, morphological differentiation can be confronted to molecular or genetic differentiation, to know to what extent morphological evolution reflects genetic evolution (e.g. Garnier et al., 2005, Magniez-Jannin et al., 2000 and Tougard et al., 2008). We evoke below some of the main results from two typical studies.

In the first example (Neige, 2003), the current biodiversity of more than one hundred of cuttlefishes (Sepiidae family) from 17 biogeographical units of the Old World is studied by means of two metrics: diversity (species richness) and disparity of cuttlebones (i.e. cuttlefish inner shells). Their shapes are quantified and compared by Procrustes methods on landmark data. One interesting result is the disconnection between diversity and disparity signals: a high number of species in a given biogeographic zone does not imply systematically high shape diversity and conversely. In two biogeographic zones (southern Africa and East India), this disconnection is particularly marked, and still remains to be explained, probably by improved knowledge of phylogenetic links between cuttlefish species.

The second example (Lefebvre et al., 2006) deals with the diversity of stylophores (i.e. atypical Paleozoic echinoderms) studied from the Middle Ordovician to the Early Silurian at the global scale. The morphological disparity of nearly 40 stylophoran species was measured by means of traditional morphometrics on plates and thecae, and compared to the signals of diversity and of “palaeogeographic dispersion” (assessed by an index quantifying the geographic occupation by species). The main results are: (i) a dissociation of the diversity and disparity signals at the beginning of the stlylophoran radiation (Middle Cambrian–Tremadocian), where the diversification of shapes precedes that of species and is reflected by the rapid but sparse occupation of the morphospace (Fig. 2); and (ii) the absence of relation between species and shape diversity, and palaeogeographic dispersion, suggesting that colonization of new habitats was not a prerequisite for stylophoran speciation and morphological differentiation.

In the two subsequent parts, we develop two promising approaches to study shape differentiation: •

by taking advantage of the very particular context of bioinvasions and the possibility of hybridations between close species (for this last point, see, for example, Renaud et al., 2009);

If bio-invasions (or biological invasions), the recent spread of a species out of their native range, are one of the major threats for biodiversity, they also provide a unique opportunity to study evolutionary changes in natura over a contemporary timescale (Stockwell et al., 2003). Mainly during the last two decades, numerous studies have examined population genetics of invasive species and the evolution of phenotypic traits suspected to play a key role in their success (Lee, 2002). Morphological traits were also seen as powerful markers to detect translocated populations and to trace their biogeographic origins (e.g. Berrou et al., 2004). However, few workers focused on the morphological diversification that can emerge following a bioinvasion phenomenon. As with any phenotypic trait, rapid morphological changes during bioinvasions probably result from three non-exclusive evolutionary processes: •

Random effects. Invasive populations are often funded from a low number of individuals. Thus, founder effects and the subsequent genetic drifts before population expansion are supposed to have a deep impact on morphological divergence (see Kolbe et al., 2007 for a documented example on Anolis lizards) ;

These potential causes for morphological divergence during bio-invasions match those generally suggested to explain evolutionary diversifications (Schluter, 2000 and Seehausen, 2004); and species invasions, seen as recent natural experiments, could allow morphologists to better discriminate their respective implications. Thus, we suggest that a morphological approach to bio-invasions should represent a fruitful field of investigation: (i) to improve our understanding of the processes governing the emergence of morphological diversity over broader time and taxonomic scales; and (ii) to help us to highlight some dark sides of the mechanisms linking genotype and phenotype during the adaptation process.

An ongoing project focuses on one of the world's worst invasive species, the tilapia Oreochromis mossambicus. Naturally restricted to few southern African rivers before the 1930 s, this cichlid fish is now introduced worldwide for aquaculture in tropical and subtropical continental waters. The large number of countries, islands and unconnected hydrological basins where O. mossambicus escaped and established itself in the wild, coupled with its abilities to survive in a broad range of ecological conditions (e.g. including gradients in salinity level, dissolved oxygen concentration, and predation pressures) (Canonico et al., 2005 and Pérez et al., 2006), make this species an ideal candidate for the study of contemporary morphological evolution. In this context, a preliminary geometric morphometrics analysis of external body shape reveals significant divergence between populations introduced approximately 50 years ago. If O. mossambicus taken as a model species provides the opportunity to study the dynamics of drift and adaptation over a contemporary time scale, it also allows the appraisal of short-term consequences on morphological variation of introgressive hybridization in the wild. Indeed, Oreochromis species easily introgress once in contact with each other. The introduction of the related species Oreochromis niloticus in the Limpopo basin (South Africa and Mozambique) and the bio-invasion of the resulting O. mossambicus x O. niloticus hybrids (D’Amato et al., 2007) provide an exciting situation to highlight the interactions between a sudden increase in genetic variation and adaptation process in a strongly structured environment. Finally, the additional interest of O. mossambicus results from the rich background in genomics and developmental biology of Oreochromis (e.g. Fujimura and Okada, 2008 and Lee et al., 2005), which should offer in the very near future the opportunity to tackle fundamental questions about the microevolution of development in order to better understand how environment acts on the genotype and on its expression to build up an integrated organism. As a second step, one can hope that the phylogenetic proximity of the Oreochromis genus with highly diverse African Cichlid species flocks (Schwarzer et al., 2009) will appear as a fruitful situation to fill some gaps between the microevolutionary process and the emergence of biodiversity.

The shape aspect considered here is the spatial organization of elementary parts of organisms, quantified by means of graph theory. It concerns the study of mathematical structures used to model pairwise relations between objects from a certain collection. Many situations can conveniently be described using a diagram consisting of a set of points with lines connecting certain pairs of these points, and graph theory has been applied to many fields of interest, among which architecture (Baglivo and Graver, 1983), social and biological sciences (Samadi and Barberousse, 2006).

Graph theory has been very seldom applied to morphological studies of biological models, but Rasskin-Gutman (2003), and Rasskin-Gutman and Buscalioni (2001) exemplified morphological applications to vertebrates, using graphs as a tool for studying shape variations and evolution of pelvic girdles and skulls. In their case studies, the boundary pattern of each skeletal element was defined by the connection to other elements. As in vertebrates, the echinoderm skeleton consists of many elements (so-called plates or ossicles), the boundary patterns of which determine the whole shape of organs and are essential in systematics and related to main evolutionary events. In the case presented herein, we show how graph theory is a relevant tool for depicting and describing apical plate patterns of a well diversified sub-group of irregular echinoids: the Spatangoida. Shape variations are not analyzed for every single plate, but shape evolution of the whole structure is studied using graph theory.

Spatangoid echinoids originate at the dawn of the Cretaceous and have been the most diversified order of echinoids ever since, counting approximately 150 fossil genera and hundreds of species. In spatangoids, there are between six and nine apical plates – located at, or close to, the top of the test – that constitute the so-called apical system, a skeletal structure involved in biological functions such as reproduction, inner pressure control and growth (new plates form in close contact with certain well-defined apical plates during growth). Consequently, the boundary pattern of apical plates has always been a concern of systematicists, and the way this pattern has changed through time is a key to understanding echinoid evolution (Kier, 1974, Néraudeau, 2001, Saucède et al., 2004 and Saucède et al., 2007).

The extensive survey of drawings and figures published for half a century (e.g. Fischer, 1966, Kier, 1974, Mortensen, 1951 and Néraudeau, 2001), along with our own observations led us to identify 24 different boundary patterns of apical plates in adult specimens of spatangoids, that is to say 24 different ways apical plates connect to each other, all apical plates considered (François, 2004). This is a very low number as compared to the 6.87 × 10¹⁰ different boundary patterns that can be constructed with nine elements and that correspond to the maximum number of possible patterns according to graph theory. Such low morphological diversity suggests very strong constraints. Among those constraints, the most pregnant comes from the fact that plates are physical entities with a given surface and cannot be totally freely organized. However, some others are inherited from the history of clades and bear a phylogenetic signal.

To describe and explore the disparity of spatangoid apical systems, boundary patterns of each type of apical system were symbolized in a graph, with plates coded as vertices and connections between plates as edges (Fig. 3A).

Preliminary results (François, 2004) show that: •

certain intraspecific and interspecific morphological variations may overlap, sometimes questioning systematics at the species and genus level;

In symmetric structures (bilateral for most organisms), the observation of deviation from this symmetry can give valuable information on the developmental stability of organisms (i.e. the result of processes which resist perturbations affecting developmental trajectories -or buffer them- within a given environment). Several types of morphological right-left asymmetry are defined (see Palmer and Strobeck, 1986), and the levels of one of them, fluctuating asymmetry, may depend both on genetic properties of organisms and on the magnitude of environmental stresses occurring during development. Morphometric methods used to detect asymmetries are either based on linear distances, or on landmark data (for a discussion on the possible biases of fluctuating asymmetry detection, see Stige et al. (2006)). We sum up below the main results of four works to exemplify the relevance of asymmetry studies (for further applications of asymmetry studies on morphological data see Debat et al., 2000 and Garnier et al., 2006).

The impact of anthropization of environment was assessed in voles (Marchand et al., 2003) and in sea urchins (Saucède et al., 2006). In the former work (Marchand et al., 2003), four populations of bank voles (Clethrionomys glareolus) were sampled near the Mont-St-Michel Bay (France). Three of them were characteristic of fragmented and intensively farmed landscapes, supposed to decrease genetic diversity in populations and to increase stress during individual development. Another population came from a less anthropized area (hedged farmland). Measures of fluctuating asymmetry on skulls and teeth confirmed this hypothesis of stress, as populations from intensively farmed areas exhibited a higher degree of fluctuating asymmetry than the population from the less disturbed area. In (Saucède et al., 2006), two populations of the sea urchin Echinocardium flavescens from Norwegian coasts were studied. One of the two populations was marked by a polluted environment. Fluctuating asymmetry levels were mainly quantified from plates from the ambulacra. The highest levels of fluctuating asymmetry were exhibited by the population living in the most stressing habitat. An originality of this work is the use of bilateral symmetry to detect asymmetries, rather the more intuitive pentaradial symmetry for echinoderms. This choice is discussed in the light of knowledge about urchin development.

Environmental stresses affecting organism development can also be of biological origin. Indeed, in Alibert et al. (2002), the effect of the presence of two acanthocephalan parasite species (Pomphorhynchus laevis and P. minutus) on the development of their intermediate host (the gammarid Gammarus pulex) was assessed. The main results are: (i) higher levels of fluctuating asymmetry in infected individuals, suggesting that the infection could act as a significant stress affecting gammarids during their development; and (ii) higher level of fluctuating asymmetry in males than in females, discussed in terms of sexual selection.

Finally, the genetic basis of developmental instability has also been considered through a review of the literature focusing on the relationship between fluctuating asymmetry and hybrid dysgenesis (Alibert and Auffray, 2003). This survey has confirmed the prominent role that genomic coadaptation can play in developmental stability and therefore the interest of such morphological approaches for the study of population differentiation and speciation. However, it also points out that predictions remain difficult to make, because the outcome depends on several factors such as the type of genomic interactions acting in hybrids or the nature of traits studied.

Modularity is defined by the fact that organisms are divided into biological parts which are hierarchically structured and partially integrated to ensure coherence, and these parts evolve more or less independently from the rest of organisms (Bolker, 2000, Cheverud, 1996 and Wagner, 1996). Whereas most modularity and integration studies on mammals have dealt with skulls (e.g. Cheverud, 1995, Drake and Klingenberg, 2010, Goswami, 2006, Hallgrímsson et al., 2004, Marroig and Cheverud, 2001 and Mitteroecker and Bookstein, 2008) and mandibles (e.g. Klingenberg et al., 2003, Márquez, 2008, Monteiro et al., 2005 and Zelditch et al., 2009), a recent study focused on teeth, and particularly on the vole lower molar row (Laffont et al., 2009). The characterization of the degree of developmental integration/modularity of sets of morphological traits can be performed by studying patterns of covariation within and among individuals from landmark data (Klingenberg, 2009). This method also assesses the developmental causes of integration/modularity patterns (Fig. 4A). By applying this approach to vole molars (Laffont et al., 2009), results have suggested: (i) quasi-independence of each molar shape at the developmental level (developmental modules), even slightly stronger for the third molar, as demonstrated by genetic and developmental hypotheses; and (ii) more pervasive integration processes among molars at the morphological level.

Additionally, a model established from murine dental development (Kavanagh et al., 2007) has recently been proposed to predict evolutionary patterns in lower murine teeth and has been extrapolated in extant and fossil mammalian species (Polly, 2007). Changes in inhibitor or activator produce modifications in molar tooth proportions and lead to different morphotypes. However, some taxa do not fit the model (Polly, 2007), such as voles, due to their oversized first lower molar. In a recent work (Renvoisé et al., 2009), the scope of the macroevolutionary model was broadened by projecting a time scale on to the developmental model (as suggested by Raff, 2007), including extant, fossil and extinct species of voles but also of other rodent families (Fig. 4B). It was demonstrated that arvicoline (i.e. voles and lemmings) evolution is rather marked by a large gap from the oldest to more recent genera with a rapid acquisition of a large first lower molar contemporaneous to their radiation. A new model was described that can characterize nonlinear molar proportions in mammals. This work underlined the necessity of adding fossil data to evolutionary developmental studies to highlight macro-evolutionary trajectories through time.