Falco

Sievwright, Holly & Macleod, Norman, 2012, Eigensurface analysis, ecology, and modelling of morphological adaptation in the falconiform humerus (Falconiformes: Aves), Zoological Journal of the Linnean Society 165 (2), pp. 390-419 : 395-397

Falco Accipiter Gyps sparverius cooperii africanus lines and surfaces in a biologically reasonable manner, the results of this operation would not differ greatly from those of our geometrically more conservative approach. By opting for a dense semilandmark sampling grid in order to include smallscale features in the analysis, we have automatically reduced the error due to topological non-alignment to a very small value. This can be done without having to resort to the shape distortions that result from the current convention of sliding 3D semilandmarks along tangents to the surface, rather than along the surfaces themselves, to the position of minimum bending energy, which is itself a biologically artificial limiting protocol.

PHYLOGENETIC MODELLING

To examine the extent to which phylogenetic relationships among higher taxonomic groupings were linked to patterns of shape variation, the phylogenetic generalized least squares (PGLS) technique of Martins & Hansen (1997) was used to subdivide the total covariance matrix (Cov total) into factors attributable to phylogenetic and non-phylogenetic sources:

Cov total = Cov phylogenetic + Cov non-phylogenetic (1.1)

Contrary to much of what has been written about various comparative methods (e.g. Gittleman & Kot, 1990; Harvey & Pagel, 1991; Gittleman & Luh, 1992; Purvis, Gittleman & Luh, 1994; Westoby, Leishman & Lord, 1995; Harvey et al., 1996 [and chapters therein]; Desdevises et al., 2003; Beauchamp & Fernandez-Juricic, 2004), numerical procedures such as PGLS, phylogenetic independent contrasts (PIC) and phylogenetic autocorrelation (PA) are not statistical techniques that remove trait variation patterns correlated with phylogeny from numerical datasets. Rather, these are modelling procedures that, given conformance of the data at hand to the assumptions of various evolutionary process models, are capable of more accurately estimating the standard errors of trait or measurement data. It is this improvement in accuracy that provides a more powerful basis for both the assessment and the statistical testing of associations between traits (for a comprehensive and critical review of approaches to comparative method analysis, see Rohlf, 2001, 2006). These improvements in data analysis results will often be obtained even if the phylogeny is not known to a high degree of accuracy.

In our investigation the cladogram of phylogenetic relationships between major bird groups calibrated against molecular data (see Fig. 2 ) was used as the basis for the comparative analysis, with branch lengths set to reflect relative assessments of a lineage’s divergence from its sister group. Scores on a number of eigensurface shape vectors sufficient to represent 95% of the observed shape variation were used to calculate lineage mean values and associated standard errors. From these data, Emilia Martins’ COMPARE software was used to model the (phylogenetically) standardized contrasts for the 12 internal nodes of the cladogram using the PIC and PGLS methods.

For both datasets a simple exponential model of constraint was applied with the strength of the constraint on phenotypic evolution estimated via a maximum-likelihood search procedure (see Martins and Hansen, 1997 and online Help documentation for COMPARE: http://www.indiana.edu/~martinsl/ compare). Two methods of modelling the phylogenetic component of the shape variation data were used to determine whether the results were robust to changes in the assumptions and methods of the modelling procedure. Based on the results of these analyses a covariance matrix of the standardized contrasts between the terminal branches was determined. This, in turn, was used as the basis for a standardized contrasts principal components analysis (PCA) and standardized contrasts canonical variates analysis (CVA) with the purpose of the latter being to determine whether it was possible to separate ecological groups using only the information included in the non-phylogenetic partition of the total covariance matrix.

ECOLOGICAL INFERENCES

Each species was assigned to ecological categories based on a compilation of data and observations provided by the Handbook to the Birds of the World ( Del Hoyo, Elloit & Sargatal, 1994), Raptors of the World ( Ferguson-Lees & Christie, 2001), Eagles, Hawks and Falcons of the World ( Brown & Amadon, 1968), the International Union for Conservation of Nature (IUCN) Red List of Threatened Species (http:// www.iucnredlist.org last accessed 1 September 2009), the Global Raptors Information Network (http:// www.globalraptors.org last accessed 1 August 2011) and Natureserve Explorer (http://www.natureserve. org/explorer/ last accessed 1 September 2009). The definitions of all ecological categories used in this study are presented in Table 1.

Figures

Figure 2. Phylogeny of Falconiformes based on Griffiths et al. (2004), Lerner & Mindell (2005), Lerner et al. (2008) and Griffiths et al. (2007). Species are grouped by their ecological or vernacular names. Size of the wedges indicates species richness. Genus or species names of taxa, along with the number of species from each genus included in the study dataset, are indicated after each clade name. Specimens were selected to be representative of overall morphological, ecological, and behavioural diversity within their group. Lineages shown in grey were not included in this investigation.