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Wrote the paper: KAY JS OS. Conceived the study: KAY. Designed the study: KAY OS. Collected and Analyzed the data: KAY. Wrote the paper: KAY OS.

The authors have declared that no competing interests exist.

Deterministic evolution, phylogenetic contingency and evolutionary chance each can influence patterns of morphological diversification during adaptive radiation. In comparative studies of replicate radiations, convergence in a common morphospace implicates determinism, whereas non-convergence suggests the importance of contingency or chance.

The endemic cichlid fish assemblages of the three African great lakes have evolved similar sets of ecomorphs but show evidence of non-convergence when compared in a common morphospace, suggesting the importance of contingency and/or chance. We then analyzed the morphological diversity of each assemblage independently and compared their axes of diversification in the unconstrained global morphospace. We find that despite differences in phylogenetic composition, invasion history, and ecological setting, the three assemblages are diversifying along parallel axes through morphospace and have nearly identical variance-covariance structures among morphological elements.

By demonstrating that replicate adaptive radiations are diverging along parallel axes, we have shown that non-convergence in the common morphospace is associated with convergence in the global morphospace. Applying these complimentary analyses to future comparative studies will improve our understanding of the relationship between morphological convergence and non-convergence, and the roles of contingency, chance and determinism in driving morphological diversification.

Adaptive radiations are important sources of biodiversity, yet uncertainty persists over the degree to which such diversity results from deterministic evolution, phylogenetic contingency, and the chance ascension of different ridges in the adaptive landscape. Though relevant microevolutionary hypotheses can be tested experimentally, the macroevolutionary process of adaptive radiation in nature is best studied by comparing patterns of morphological diversity among replicate radiations of related lineages diversifying in similar environments

Examples of convergent adaptive radiations in nature include fish from post-glacial lakes, frogs and mammals from different continents, and lizards and spiders from oceanic islands

The endemic cichlid fish assemblages of Lakes Victoria (LV, ≥450 sp.), Malawi (LM, ≥450 sp.) and Tanganyika (LT, ≥200 sp.) are the most speciose and ecologically diverse radiations known and uniquely suited for a comparative study of adaptive radiation. The fish communities of all three lakes are dominated by endemic assemblages that display qualitatively convergent sets of ‘ecomorphs’ occupying nearly every imaginable niche

We first show that when compared in a common morphospace the assemblages of endemic cichlid fishes from the three lakes show evidence of non-convergence. We then analyze patterns of morphological diversity for each assemblage independently and find that the assemblages are diversifying along common axes through the global morphospace. Together these analyses help resolve an apparent empirical discord between of convergence and non-convergence and offer a promising approach for improving our ability to determine the roles of chance, contingency and determinism in adaptive radiation.

We collected digital images of the left side of representative individuals from the collections of the Natural History Museum (London, U.K.), Africa Museum (Tervuren, Belgium), Naturalis Museum (Leiden, Netherlands) and the personal collection of O.S. Importantly, Lake Victoria cichlids were sampled from collections made prior to wide spread extinctions associated with eutrophication and population expansion of introduced Nile perch (

(1) anterior tip of lower jaw, (2) posterior tip of lower jaw , (3) posterior hinge of lower jaw, (4) ventral-posterior extreme of mandible plate, (5) ventral-posterior extreme of preopercle, (6) dorsal end of preopercle just below the pterotics, (7) dorsal margin of the head directly above the centre of the eye, (8) dorsal margin of the head directly above (6), (9) posterior extreme of gill-cover at opercular blotch, (10) anterior insertion of dorsal fin, (11) posterior insertion of dorsal fin, (12) dorsal insertion of caudal fin, (13) caudal border of hypural plate at the lateral line, (14) ventral insertion of caudal fin, (15) posterior insertion of anal fin, (16) anterior insertion of anal fin, (17) anterior/dorsal insertion of pelvic fin, (18) ventral insertion of pectoral fin, (19) dorsal insertion of pectoral fine, (20) anterior extreme of snout bone, (21) end of opercular membrane ventrally.

We used partial warp analysis in tpsRelw version 1.42

We first followed the traditional comparative approach by including all 375 specimens in morphometric analyses of total shape (landmarks 1–21), body shape (9–19), head shape (2,7–9,20, 21), and jaw shape (1–6). We used tpsRelw to conduct principal components analysis (PCA) on the matrix of partial warp weights to yield relative warp scores, the equivalent of PCA scores for geometric morphometric data. From each analysis we retained the four relative warp axes that explained more than 5% of the variation in morphology. These axes are hereafter referred to as _{max}-M_{4}

We compared patterns of diversity in the common morphospaces using a new approach we call the ‘ordered-axis plot’. Ordered-axis plots are constructed and analyzed as follows (

Ordered-axis plots discriminate between different patterns of morphological diversity along axes of a multidimensional morphospace. In this example species of two adaptive radiations with the same number of observations are represented by clouds of red (older, more diverse) and blue (younger, less diverse) points in two dimensional morphospaces defined by M_{max} and M_{2}. When their values along an axis are independently ordered from smallest to largest then combined to form a set of _{max} the radiations are centered at the same point (i.e. convergent) so the int. = 0, and equally diverse, so the slope = 1; (B) along M_{2} the radiations are again centered at the same point (convergent, int. = 0) but the older radiation is more diverse so the slope of the regression of _{max} the radiations are centered at different points along the axis (non-convergent, int.≠0) but have equal levels of diversity (slope = 1); (D) along M_{2} the radiations are non-convergent (int.≠0) and the older radiation is more diverse (slope<1).

Ordered-axis plots have two advantages over using means and variances to test for differences in location and diversity, respectively, along axes of a common morphospace. First, they compare relative location and diversity using a single analysis associated with a simple visual representation. Second, the intercept and slope of ordered-axis plot regressions are more sensitive to extreme morphologies than tests for the equality of means and variances. Because our samples, like the assemblages themselves, are dominated by average rather than extreme phenotypes, this sensitivity is particularly important for testing whether assemblages are centered at different locations and have different levels of morphological diversity along different axes of morphospace. For comparison, for each of the 16 axes analyzed using ordered-axis plots we present the results of pairwise parametric tests for equal means (

In all our analyses the 125 values from LT, which is the oldest and most morphologically diverse assemblage, are placed on the _{max}-M_{4}

Comparing patterns of diversity in a common morphospace requires that the diversities of the assemblages are summarized along common axes, even if the true axes of diversification actually vary among assemblages. We removed this constraint by analyzing each assemblage separately, which allows the axes of morphological divergence to be defined independently for each assemblage. We then compared these axes of diversification to test whether the three assemblages are diversifying in parallel through the unconstrained global morphospace.

We recalculated the same four partial warp matrices (total, body, head and jaw shape) for each assemblage separately and conducted PCA on each partial warp matrix to yield relative warp scores. For each assemblage we again retained _{max}-M_{4}_{max}

The results of global morphospace analysis suggest that body, head and jaw shape covary similarly in the three assemblages. To formally test the hypothesis that the different elements of total shape covary similarly we further decomposed body, head and jaw shape into three, two and two sub-elements, respectively [upper body (9–11), caudal area (11–15), lower body (16–18), upper head (7–9), lower head (9,20,21), cheek (3–6), and lower jaw (1–3)(_{max}_{max}_{max}

The common morphospace analysis provides three insights (_{max}_{2}_{max}_{max}-M_{4}

Variation in body, head and jaw shape diversity in common morphospaces among the cichlid assemblages from Lakes Victoria (LV-green), Malawi (LM-blue) and Tanganyika (LT-pink). (A) Locations of species of the three assemblages in the three morphospaces. (B) Ordered-axis plots along M_{max} and M_{2} (with LT along the _{max} axes. For these plots the approximate ages of the assemblages are: LV-0.1 myr., LM-2 myr., LT-10 myr. Note that the lines connecting the points are included for comparison, not to imply temporal trends in diversity of a single radiation.

axis | total shape | body shape | head shape | jaw shape | ||||||||

% | slope | int. | % | slope | int. | % | slope | int. | % | slope | int. | |

_{max} |
32 | v<m<1 (v<m = t) | 0<m = v (t<m = v) | 47 | v<m<1 (v<m = t) | 0<v = m (t<v = m) | 49 | v<m = 1 (v<m = t) | 0<v<m (t<v = m) | 53 | m = v<1 (m<v = t) | v<0<m (v<t = m) |

_{2} |
21 | v = m = 1 (v = m = t) | v<0<m (v<t = m) | 15 | v<m = 1 (v<m = t) | m<0<v (m = t<v) | 17 | v<m<1 (v<m = t) | m<0<v (m = t<v) | 26 | v<m<1 (v<m = t) | v<m<0 (v = m = t) |

_{3} |
13 | m<v<1 (m<v = t) | 0<m = v (t<m = v) | 11 | v<m<1 (v = m<t) | m<v<0 (m = v = t) | 16 | v = m<1 (v = m = t) | 0<m<v (t = m = v) | 10 | v<m = 1 (v<m = t) | m<v<0 (m = v = t) |

_{4} |
5 | v<m<1 (v<m = t) | v<0<m (v<t<m) | 8 | v = m<1 (v = m<t) | m = v<0 (m = v<t) | 7 | v = m,m = 1 (v = m = t) | 0<v<m (t = v = m) | 6 | v = m<1 (v = m = t) | v<0<m (v<t<m) |

Second, morphological diversity appears to accumulate continually and be unrelated to species richness. For all but three of the16 axes the rank order of diversity (i.e. slopes of LM and LV on LT with LT = 1) matches that of assemblage age (_{max}_{2}_{max}

Finally, morphological diversity in head and jaw shape appears to accumulate faster than in body shape. Whereas shape diversity is age-ordered along _{max}_{max}_{max}

The assemblages are diverging in parallel through the unconstrained global morphospace along every _{max}_{max}_{max}

Each element of shape (body, head, jaw) was analyzed separately for each assemblage (colors as in _{max} axis. See

dimensions | total shape | body shape | head shape | jaw shape | ||||||||

t-m | t-v | m-v | t-m | t-v | m-v | t-m | t-v | m-v | t-m | t-v | m-v | |

_{max} |
41.9 | 59.1 | 19.5 | 20.7 | 15.8 | 9.8 | 22.2 | 17.1 | 14.2 | 17.3 | 23.9 | |

2, 127° | 73.2 | 75.4 | 78.3 | 60.3 | 64.9 | 57.4 | 82.5 | 34.9 | 20.5 | 30.0 | ||

3, 156° | 58.4 | 66.8 | 44.2 | 23.1 | 34.7 | 34.2 | 21.5 | 50.4 | ||||

4, 180° | 86.4 | 68.1 | 66.5 | 30.0 | 37.3 | 34.1 | 12.2 | 18.1 | 21.9 |

The angles between the assemblages are consistently higher for total shape than for body, head and jaw shape (_{max}_{max}_{max}_{max}_{2}

Not only are the assemblages diverging in parallel through the global morphospaces, but as _{max}

Matrix correlation plot of the elements (_{ij}_{ij}_{ij}_{ij}

The endemic cichlids assemblages of the three African great lakes are a famous example of convergent evolution where the same sets of ecomorphs have evolved independently in each basin

The non-cichlid communities of LV and LM are similar, whereas that of LT is more speciose and contains an endemic pelagic community. If community composition of non-cichlids strongly constrains patterns of morphological diversity, the assemblages of LV and LM should be similar and more diverse than the LT assemblage. There is some evidence for the first pattern and clearly none for the second. LV and LM have the same intercept along four axes of the common morphospace, yet along no axis does either have the same intercept as LT (

Phylogenetic contingency and evolutionary chance may result in non-convergence through at least three non-exclusive mechanisms. The first invokes colonization history directly. The LT assemblage contains several phylogenetically independent radiations originating from different colonizing lineages, one of which gave rise to the haplochromine ancestors of the LM and LV radiations

Our second analysis suggests any non-convergence in the common morphospace is not the result of the assemblages diversifying along different axes through the global morphospace. Rather, the two analyses together reveal that despite differences in ecological context and phylogenetic history, and the inevitable contribution of chance that combine to produce non-convergence in a common morphospace, the cichlid assemblages of the African great lakes are diversifying in parallel through the global morphospace. Parallel divergence may be due to deterministic evolution if natural selection drives diversification along similar morphological axes in all three lakes, or phylogenetic contingency if those axes are determined by genetic constraints shared by the assemblages. The view that parallel divergence is the result of deterministic evolution rather than phylogenetic contingency is supported by the observation that the closely related and less phylogenetically diverse LV and LM radiations are not diversifying through the global morphospace along axes more similarly to each other than to the polyphyletic LT assemblage (

Our results underscore the value of comparing radiations and polyphyletic assemblages of widely different age and viewing adaptive radiation not only as an endpoint (patterns of diversity in a common morphospace) but as a process (axes of divergence through the global morphospace). Considering a celebrated example of convergent adaptive radiation highlights this point. Caribbean

The relative ages of the cichlid assemblages make our results relevant to two outstanding questions about the temporal progress of adaptive radiation

Finally, evidence that diversity in head and jaw shape accumulates faster than in body shape supports the view that diversification during adaptive radiation proceeds at trait-dependent rates

Deterministic evolution, phylogenetic contingency and chance can all influence patterns of diversification during adaptive radiation. By combining traditional and new comparative approaches we have demonstrated how apparently non-convergent patterns of morphological diversity may mask parallel patterns of morphological divergence during adaptive radiation. Considering patterns of diversity in both common and global morphospaces enhances our ability to infer the roles of determinism, contingency and chance during adaptive radiation.

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We thank the staffs of the Museum of Natural History (London, UK), the Royal Museum for Central Africa (Tervuren, Belgium), and the Naturalis Museum (Leiden, Netherlands) for hospitality and access to their cichlid collections. We thank the U Berne/EAWAG Aquatic Ecology and Macroevolution group, M.J. Genner, D.A. Joyce, G.F. Turner and B. Sidlauskas for discussions and comments.