a3-jc = y
3.4.1 Multivariate statistical methods
The morphological data were analysed using discriminant function analysis, implemented using SPSS fo r Windows (version 7.0). The craniodental data were also analysed using hierarchical cluster analysis, implemented using the same software. These forms o f multivariate statistical analysis have been employed by numerous authors, to assess morphological variability among a variety o f primate groups (e.g. Masters and Lubinsky, 1988; Froehlich et a i, 1991; Kobayashi, 1995; Ravosa, 1998; Burity et al., 1999). The techniques were selected since they can be used to identify groups o f morphological similarly in a given set o f observed measurements (Sokal and Rohlf, 1995).
Discriminant function analysis
The aim o f discriminant function analysis (DFA) is to predict group membership from a set o f independent variables having outlined a set o f grouping variables
(Tabachnick and Fidell, 1996). The independent variables are selected (in this study the metrical measurements collected from gibbon postcrania, crania and teeth), as well as the grouping variables (the eleven gibbon species) and a DFA computed to give a set o f discriminant functions. These are derived in such as way as to maximise the difference between groups relative to the variation within groups.
There are three types o f DFA: direct, sequential (also known as hierarchical) and stepwise. In direct DFA all the variables enter the analysis at once; in sequential DFA they enter according to a schedule set by the analyser; and in stepwise DFA statistical criteria determine the order o f entry. The stepwise method is the most generally
applicable (Kinnear and Gray, 1995) since in most cases, including this study, there is no reason to give some predictors higher priorities than others. The effect o f including a particular independent variable (IV) in the DFA is assessed by a statistical test, the results o f which are used as a basis for the inclusion o f that IV in the final analysis. A variety o f statistical tests are available for weighing up the inclusion, or not, o f variables; W ilks’ lambda is the most commonly used. W ilks’ lambda is a multivariate test o f significance, sometimes called the U statistic. Lambda ranges between 0 and 1, with values close to 0 indicating the group means are different and values close to 1
indicating the group means are not different. When this procedure is complete a summary table is produced indicating which variables were added or removed at each step. The variables remaining in the analysis are those used to compute discriminant functions (Kinnear and Gray, 1995).
In a DFA those discriminant functions with eigenvalues above 1 are considered the most significant. The first discriminant function accounts for the highest percentage o f variance, and has the highest eigenvalue. The higher functions account for
successively lower percentages o f the overall variance and have successively smaller eigenvalues. IV ’s that load highly on particular functions indicate that those particular variables are important in discriminating groups. IV which are particularly important (i.e. have loading greater than 0.5) or may be meaningful, are deduced from the
standardised canonical discriminant function coefficients table and the structure matrix in the output listing.
The post-hoc predicted groups membership scores provide an indication o f the success o f predicting group membership based on the discriminant functions developed in the analysis. The higher the percentage for each group, the greater the success in predicting group membership (species groupings, in this case) based on the discriminant
functions. An overall percentage is given which provides an indication o f the general success in predicting group membership.
Hierarchical cluster analysis
Hierarchical cluster analysis groups together those cases which are most similar, in a sequential fashion. In order to cluster cases it is necessary to have some numerical similarity measurement to characterise the relationships among the cases (Anderberg, 1973). This is achieved by computing a measure o f association for every pairwise combination o f the cases using an algorithm. The algorithm starts with each case in a separate cluster and combines clusters until only one is left. The basic assumption o f all cluster analysis methods is that these numerical measures o f association are comparable to each other. In hierarchical cluster analysis, such association measures are used to construct a similarity matrix. This matrix describes the strength o f all pairwise relationships among the cases. The methods o f hierarchical cluster analysis (implemented using the software SPSS fo r Windows [version 7.0]) operate on this similarity matrix to construct a tree, or dendogram, depicting specified relationships among pre-selected groups (in this case the different species o f gibbon).
Once the similarity matrix has been created there are a variety o f tree building techniques available. The simplest method is single-linkage cluster analysis (Anderberg,
1973). In this method, clusters are joined at each stage by the single shortest or
strongest link between them. The single linkage method has been adopted here since it makes the least number o f assumptions about the data.
Size correction
The question o f size and shape in comparative biology is an ongoing issue (Mosimann, 1970; Corruccini, 1973; Darroch and Mosimann, 1985; Jungers et a i,
1995; Sokal and Rohlf, 1995; and references therein). It is widely accepted that, in order to find genuine shape differences among a suite o f linear measurements representing interspecific variability among a set o f taxa, the effects o f overall size must be
controlled (e.g. Jungers, et a i, 1995). Indeed, shape differences themselves may depend on size differences (Gould, 1966). The view taken in this study is that for phylogenetic purposes, both size and shape may play an important role in distinguishing taxa,
however, in order to assess shape differences it is necessary to remove the confounding effects o f body size. Hence, is was decided to create two datasets, one comprising raw data and the other with the effects o f body size removed. In this way the results o f multivariate analyses can be compared, taking into account both size and shape differences.
Numerous size adjustment techniques have been proposed and a useful review o f the main methods can be found in Jungers et al. (1995). This paper reviews eleven size adjustment techniques. The authors applied the various size adjustment techniques to a craniometric dataset comprising several measurements from different species o f guenons. This was designed to test for successful size adjustment with reference to interspecific craniometric analysis. The procedure was also applied to a dataset comprising native American anthropometries to test the success o f size correction in relation to intraspecific analyses. Jungers et a l set the criterion that organisms o f identical shape should have no measurable distance between them after differences in size are removed. Using this criterion they attempted to identify different sized individuals o f the same shape, after the various size correction techniques had been
applied. One o f the Mosimann family o f shape ratios (Mosimann, 1970), was one o f three identified by Jungers et al. (1995) as being successful based on the criterion set out above. This method has been adopted in this study. It involves dividing each variable by the geometric mean o f all variables. One advantage o f using the geometric mean is that the standard against which the individuals are scaled is not dependant on the composition o f the sample. Furthermore, this technique allows for the effects o f size-related shape, i.e. it corrects for geometric shape differences, hence allometric shape differences remain.
3.4.1 R esults
Discriminant Function Analysis Craniodental data
Size and shape differences among the eleven gibbon species were assessed by performing two DFA, one using the raw craniodental data (reflecting both size and shape), another using the size-corrected data (emphasising shape). Each analysis produced 10 discriminant functions. The first three functions had eigenvalues over one and accounted for over 85% o f the variance in each o f the analyses (raw and size- corrected) (Table 3.4a).
The DFA using raw craniodental data produced several clear morphological groupings (Figure 3.13). Function 1 reflects size, and separates the large {syndactylus),
medium {hoolock, concolor, gabriellae, and leucogenys) and small (lar, agilis, moloch,
muelleri, pileatus, and klossii) sized gibbons. These size separations are in agreement
with previous findings (Geissmann, 1993). Function 1 accounts for over 58% o f overall variance (Table 3.4a) and is described by orbit breadth (Table 3.4b). Function 2 reflects a shape difference and separates syndactylus from the subgenus Nomascus {concolor,
gabriellae and leucogenys), and to a lesser extent klossii from lar, agilis, moloch,
muelleri, and pileatus (Figure 3.13). Function 2 accounts for a further 21% o f the
variance (Table 3.4a), and is described by the breadth o f T, the width o f PM3, and the
coronoid height o f the mandible (Table 3.4b). Function 3 separates hoolock from species in the subgenus Nomascus {concolor, gabriellae, and leucogenys) (Figure 3.14). It is described by the height o f the nose from nasion to nasospinale, lower facial
prognathism, palate length, height o f the skull between bregma and basion, and the width o f M2 (Table 3.4b).
The DFA using size-corrected craniodental data produced similar grouping patterns as the analysis using raw data. Function 1 again separated syndactylus, the larger sized gibbon, hoolock, concolor, gabriellae, and leucogenys, the medium sized gibbons, and lar, agilis, moloch, muelleri, pileatus, and klossii, the smallest gibbons (Figure 3,15). This result suggests that since size has been removed, these separations are based on shape differences o f orbit breadth and lower facial prognathism, the variables which have high standardised canonical function coefficients scores (Table 3.4c). Function 2 again separates syndactylus from the subgenus Nomascus {concolor,
gabriellae, and leucogenys), and to a lesser extent klossii from lar, agilis, moloch,
muelleri, and pileatus (Figure 3.15). This function is described by the relative breadth
o f I^, the relative height o f the skull between bregma and basion, the relative width of PM], and the relative coronoid height o f the mandible (Table 3.4c). Function 3 for the size-corrected DFA, is described by the relative height o f the nose from nasion to nasospinale (Table 3.4c), and separates hoolock from species in the subgenus Nomascus
{concolor, gabriellae, and leucogenys) (Figure 3.16). Again this is in agreement with
T a b le 3 .4a Results o f discrim inant function analyses based on craniodental data
Function Eigenvalue % o f Variance Cumulative % Canonical correlation Analysis based on raw data
1 10.18 58.18 58.18 0.95
2 3.77 21.52 79.69 0.89
3 1.59 9.06 88.75 0.78
Analysis based on size-corrected data
1 &32 54.49 54.49 0.94
2 3.41 2Z32 76.81 0 . 8 8
3 1.40 9.18 85.99 0.76
T able 3.4b Standardised canonical discriminant function coefficients for raw craniodental data
Function 1 Function 2 Function 3
Orbit breadth -.54 .49 .09
f breadth .03 .73 . 2 1
PM3 width .26 - . 6 6 .32
Coronoid height o f mandible - . 0 0 .65 -.16
Nasion to nasospinale .37 . 1 2 . 6 8
Lower facial prognathism .42 .17 -.91
Palate length .37 -.07 .54
Bregma to basion . 2 2 -.32 .63
M, width .30 -.32 -.54
T able 3.4c Standardised canonical discriminant function coefficients for size-corrected craniodental data
Function 1 Function 2 Function 3
Orbit breadth -.58 .35 - . 2 2
Lower facial prognathism .62 .34 -.40
f breadth .04 .65 .29
PM3 width .28 - . 6 6 .13
Bregma to basion .04 -.50 .45
Coronoid height o f mandible . 1 2 .65 . 0 1
Q CP
Species
+ syndactylus[1] ^ leucogenys[2] • gabriellae [2] ^ concolor [2] hoolock [3] ■ Wosai [4] ^ pileatus[4] ^ muelleri [4] ^ moloch [4] O agilis[4] ° lar [4]Function 1
Figure 3.13 Scatter plot o f discriminant function 1 against discriminant function 2 for the analysis o f raw craniodental data.
[1] subgenus Symphalangus, [2] subgenus Nomascus, [3] subgenus Bunopithecus,