Figure 1.
The temporal trajectories of taxonomic diversity, morphological disparity and morphological integration of Phanerozoic crinoids.
(A) Number of genera known and number of species sampled per genus per stratigraphic interval. (B) Disparity measured as the sum of univariate variances; integration measured as the relative standard deviation of the eigenvalues of the correlation matrix. (C) Disparity measured as the mean character dissimilarity; integration measured as mean mutual compatibility. Error bars are bootstrapped standard errors. Because low sample sizes prevent from deriving reliable estimates of correlation matrices (see text), integration values are not presented for Early Ordovician, Late Permian, Triassic, and Cenozoic data. Whether based on the analysis of discrete or continuous variables, variations in the overall degree of integration do not appear to be associated with concomitant changes in disparity.
Figure 2.
Correlation between temporal changes in disparity and integration.
Spearmann’s rank correlation between level of morphological disparity and degree of morphological integration. (A) Generalized differences of morphological integration versus disparity for the PCoA-based approach (black circles; r = −0.118, P = 0.609) and the discrete character approach (open circles; r = −0.449, P = 0.042) when all characters are considered. (B) Generalized differences of morphological integration versus disparity for the PCoA-based approach (black circles; r = −0.340, P = 0.131) and the discrete character approach (open circles; r = 0.118, P = 0.609) when only taxonomically non-significant characters are considered (see text). In general, the amount of morphological disparity displayed by crinoids is not significantly correlated with the overall degree of integration among morphological traits.
Figure 3.
The temporal trajectory of integration patterns of Phanerozoic crinoids.
The plot shows the first three principal coordinates of the space of correlation matrices. Each point corresponds to the correlation matrix of crinoids within a given geologic time interval (The correlation between pairwise Euclidean distances in the space of the first three principal coordinates and the actual distances between correlation matrices is 0.85). The grey line represents the temporal trajectory of correlation matrices from the Ordovician (O2) to the end of the Cretaceous (K4), and the asterisk gives the location of the identity matrix (i.e., a matrix with no integration among traits). Dotted lines are 68% confidence ellipses based on bootstrap resampling. Labels: O2 = Llanvirnian to lower Caradocian, O3 = remainder of Ordovician, LS = Lower Silurian, MS = Middle Silurian, US = Upper Silurian, LD = Lower Devonian, MD = Middle Devonian, UD = Upper Devonian, T = Tournaisian (Carboniferous, Mississippian), Sr = Serpukhovian (Carboniferous, Mississippian), B = Bashkirian (Carboniferous, Pennsylvanian), M = Moscovian (Carboniferous, Pennsylvanian), St = Stephanian (Carboniferous, Pennsylvanian), P1 = Asselian-Sakmarian (Permian), P2 = Artinskian-Kungurian (Permian), LJ = Lower Jurassic, MJ = Middle Jurassic, UJ = Upper Jurassic, K1 = Neocomian (Cretaceous), K2 = Barremian-Aptian (Cretaceous), K3 = Albian-Turonian (Cretaceous), K4 = Senonian (Cretaceous). The first principal coordinate separates Palaeozoic from post-Palaeozoic forms. The distribution of most Palaeozoic correlation matrices near the identity matrix emphasizes their homogeneous structure (roughly similar pairwise correlation among traits), whereas post-Palaeozoic correlation matrices display individuated blocks of correlated traits.
Figure 4.
Matrices of mutual compatibility for Palaeozoic and post-Palaeozoic crinoids.
These two matrices exemplify the differences in patterns of integration between (A) Palaeozoic (Middle Devonian, MD) and (B) post-Palaeozoic crinoids (Upper-Jurassic, UJ). The choice for these two time intervals has been driven by their location in the space of correlation matrix (separation along PCo1; see Figure 3) and the comparability of their sets of applicable characters (number and distribution over the whole character matrix). The gray-scale correlates with the strength of mutual compatibility (∼correlation): the darker the gray, the higher the compatibility. The comparison of these two matrices shows the overall stronger integration among characters within the post-Palaeozoic matrix and its heterogeneous structure with larger blocks of compatible characters (e.g., stem and dorsal cup characters, arm and dorsal cup characters).