A Statistical Framework for Testing Modularity in Multidimensional Data

Márquez, Eladio J.

doi:10.1111/j.1558-5646.2008.00476.x

Cited by 66 publications

(109 citation statements)

References 81 publications

(118 reference statements)

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“…This a priori partitioning places a premium on the recognition and biological significance of partition boundaries, and taking the shapes out of context of the whole ignores integration due to position and relative size of the partitions. Although boundaries between these partitions can be defended on biological grounds, future studies could employ methods that do not depend on such a priori partitioning (Márquez 2008;Klingenberg 2009). Third, functional integration may have played a larger role than was detected herein, because our model of functional integration is simple and could be refined.…”

Section: Discussionmentioning

confidence: 98%

Evolutionary Lability of Integration in Cambrian Ptychoparioid Trilobites

Webster

Zelditch

2011

Evol Biol

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Phenotypic integration can influence evolutionary rate and direction by channeling variation into few dimensions. The extent to which that channeling serves as a constraint over macroevolutionary timescales is determined in part by the evolutionary lability of phenotypic integration. Evolutionary change in patterns of pleiotropy, potentially reducing that constraint, is thought to be more readily achieved when pleiotropy is structured by variation arising in parallel along different developmental pathways rather than by variation arising from direct interactions within and between those pathways. Herein we test two predictions that follow from that hypothesis: (1) that clades undergoing dramatic diversification are characterized by integration that is weakly influenced by direct interactions; and (2) that the structure of integration arising from direct interactions is more conservative than that arising from parallel variation. We examine integration of the cranidium of two Cambrian ptychoparioid trilobites, Crassifimbra walcotti and Eokochaspis nodosa, comparing them to each other and to a previously studied species, C.? metalaspis. Shape variation is decomposed into components representing variation among individuals and variation due to direct interactions. In all three species, variation among individuals was only weakly influenced by direct interactions, suggesting that integration was unlikely to have been a long-term constraint on the Cambrian diversification of ptychoparioids. Phenotypic integration of E. nodosa is no more similar than expected by chance to either Crassifimbra species, but the component due to direct interactions is more similar than expected by chance to that of C.? metalaspis. Conversely, the two Crassifimbra species are generally similar (although not identical) in phenotypic integration, but markedly differ in their structure of direct interactions. Integration arising from direct interactions was therefore not immune to restructuring over even short evolutionary timescales, and was not always more conservative than that arising from parallel variation.

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Section: Discussionmentioning

confidence: 98%

Evolutionary Lability of Integration in Cambrian Ptychoparioid Trilobites

Webster

Zelditch

2011

Evol Biol

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“…The best fitting model is the one that deviates least from the data taking into account the number of fixed parameters. The c* is scaled as a function of the maximum c value (calculated from a null model of no integration), and scaled a second time to account for the number of fixed parameters (Marquez 2008). This last step is performed by regressing the c values on the number of fixed parameters, since both are linearly related (Marquez 2008).…”

Section: Minimum Deviance Methodsmentioning

confidence: 99%

“…The fit of the hypotheses is assessed through the standardized gamma statistic (c*), a measure of the deviance between the model and the data (Richtsmeier et al 2005;Marquez 2008). For the hypotheses, modules comprising subsets of landmarks are made statistically independent by placing them into orthogonal subspaces; intramodular covariances are estimated from the data (Marquez 2008). The null hypothesis is that the difference between the observed and expected covariance matrices is no greater than expected by chance; thus, a low p value indicates that the model fits the data poorly (Parsons et al 2012).…”

Section: Minimum Deviance Methodsmentioning

confidence: 99%

Head, Body and Fins: Patterns of Morphological Integration and Modularity in Fishes

2015

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Actinopterygians demonstrate high levels of morphological disparity, especially in the variation of fin positions, sizes and shapes. One hypothesis to explain the diversity of fin morphologies is that it is facilitated by a modular organization. According to this hypothesis, fin modules would be quasi-independent during ontogeny or evolution, facilitating their evolvability. We investigated variational modularity of fins in two cyprinid species, the zebrafish (Danio rerio) and the Northern redbelly dace (Chrosomus eos), to determine which subsets of fins are quasi-independent and which are most highly integrated in positioning. Hypotheses of modularity were evaluated using a combination of methods suitable for analyses of landmarks. The hypothesis that the dorsal and anal fins belong to a posterior trunk and tail module is strongly supported, a finding that can be explained by the use of subcarangiform locomotion in these two species. There is also some support for the hypothesis that the paired fins and head region each constitute variational modules. The support for fin variational modules is weaker than expected considering the wealth of developmental evidence supporting fin modularity. This might be related to a dissociation of the fin positioning modules during actinopterygian evolution, a process that had already been suggested for the dorsal and anal fins. Alternatively, the fin modules inferred from developmental data might not directly translate into variational modules: variational modules can incorporate the signals from numerous partially overlapping developmental processes so that one to one correspondence between developmental and variational modules is not always expected.

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“…Interspecific variation in carnivoran mandible shape primarily reflects differences at the family level, and secondarily adaptation to distinct feeding habits. However, we do not know to what extent this applies to distinct mandibular subunits, given these structures (the corpus and ramus) are expected to be affected by the tight developmental correlation of parts that integration requires (Cardini 2003;Klingenberg and Leamy 2001;Klingenberg et al 2003;Monteiro et al 2005;Márquez 2008;Monteiro and Nogueira 2009).…”

Section: Introductionmentioning

confidence: 94%

Phylogenetic signal, function and integration in the subunits of the carnivoran mandible

et al. 2011

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Complex phenotypes could be interpreted as the result of functional integration between identifiable subunits. Common developmental or ecological factors may favour macroevolutionary morphological integration so that functional subunits also covary above the species level. We investigate shape variation and functional integration in two subunits of the mammalian mandible: the corpus and the ramus in a subset of extant terrestrial Carnivora using geometric morphometric and comparative methods. More specifically, we test if corpus and ramus shape exhibit similar degree of homoplasy and if these traits covary above species level. Additionally, broad functional categorisations (predaceous and non predaceous) are investigated to test if differences in morphological variation and integration at macroevolutionary scale occur. Principal components of shape data show a significant phylogenetic signal in both mandibular subunits, with the ramus exhibiting a higher degree of homoplasy than the corpus. Functional groups (predators and non-predators) are significantly distinct in corpus shape, while in the ramus significance emerges only after removing the phylogenetic signal. Partial Least Square shows that mandibular corpus and ramus region covaries above species level even if this trend is not supported when employing comparative methods. Only in a subset of predaceous species covariation still hold. We conclude that mandibular subunits of Carnivora differ considerably in shape among predaceous and non-predaceous species because of the adaptive selection pressure imposed by catching and hold of live prey. This selective process also favoured macroevolutionary integration in predaceous carnivorans.

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A Statistical Framework for Testing Modularity in Multidimensional Data

Abstract: Within species, these modules are embedded within larger "super-modules," suggesting that these conserved modules act as building blocks from which covariation patterns are built.

Cited by 66 publications

References 81 publications

Evolutionary Lability of Integration in Cambrian Ptychoparioid Trilobites

Evolutionary Lability of Integration in Cambrian Ptychoparioid Trilobites

Head, Body and Fins: Patterns of Morphological Integration and Modularity in Fishes

Phylogenetic signal, function and integration in the subunits of the carnivoran mandible

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