4.2 Methodology
4.2.4 Shell Morphology and Morphometrics
4.2.4.1 Characters selected for Shell Morphometric Analysis
Morphometric shell characters were chosen based on their representation in previous studies on shell morphometrics and their ability to provide a comprehensive
characterisation of shell morphology (Pace, 1973; Brandt, 1974; Liu et al., 1979, Burch, 1980; Lam and Calow, 1988; Chiu et al., 2002). To assess the morphology of R.
rubiginosa and L. natalensis shells (Figure 4.4) in a repeatable, objective fashion, a traditional morphometric approach was used.
Figure 4.4: Representatives of the family Lymnaeidae, identified from the study areas.
A – Lymnaea natalensis Krauss, 1848, scale bar 10 mm B – Radix rubiginosa (Michelin, 1831), scale bar 10 mm
Shells of two size classes were selected (shell length < 10 mm and shell length ≥ 10 mm).
An initial suite of six characters for each specimen was measured and used to describe the within-group and between-group variability for the two lymnaeid species. Shell characters were measured to the nearest 0.01 mm using a graticuled eyepiece on a Leica stereomicroscope and a 20 cm vernier caliper. To avoid the effects of bilateral
asymmetry, bilateral characters were measured on the right hand side of the shell.
Measurements were taken from reference points as denoted in Figure 4.5 for the six characters: shell length (SL), shell width (SW), aperture length (AL), aperture width (AW), length of last body whorl (LBW) and spire height (SPH).
A B
Figure 4.5: Schematic drawing of the six shell characters used for the traditional morphometric approach.
AL – aperture length; AW – aperture width; LBW – length of last body whorl; SL – shell length; SPH – spire height; SW – shell width.
4.2.4.2 Statistical Morphometric Analyses
(a) Error Measurements
Within any study utilising morphometric data, variation in characters among populations SL
SW
AW
AL LBW
SPH
that often confound true taxonomic and evolutionary relationships (Pankakoski et al., 1987; Richards, 2007). Measurement error describes that component of non-heritable morphological variation arising from variability of repeated measurements of a particular character taken on the same individual, relative to its variability among individuals in a particular group (Bailey and Byrnes, 1990).
According to Bailey and Byrnes (1990), repeatability of measurements of a particular character varies depending on the level of precision relative to the total variability among individuals in a particular group. Precision, in this sense, is described as the „closeness‟
of repeated character measurements to each other and is considered the converse of measurement error (Taylor et al., 1990; Zar, 1999). Furthermore, a term often incorrectly used in synonymy with precision is accuracy, which describes the „closeness‟ of a
measurement to the actual value of the character measured (Zar, 1999).
To assess the associated error levels, 30 individuals with a complete suite of shell characters were randomly chosen, five individuals from each of the three study sites and the two size classes. As a test of measurement error, the six shell characters were measured once a day for three days. The series of three measurements were thus independent of each other and allowed the measurement error to be assessed.
Percentage measurement error (%ME) is the within-individual error relative to the between-individual error, and was calculated using methods outlined in Pankakoski et al.
(1987). Mean within-individual coefficients of variation were calculated for each individual and character, using arithmetic means and standard deviations. According to Pankakoski et al. (1987), the effects of differences in character means between the 30 individuals were excluded by calculating separate coefficients of variation for each individual, for each character measurement (CVc). The overall within-individual error (CVWI) corresponded to the means of the 30 individual CVc measurements. The overall between-individual error (CVBI) was calculated from the total variability of each of the three replicates of character measurements for the 30 individuals.
The primary objective, using repeated measures of the shell characters, was to assess the associated error levels. This was done to ensure that only characters with low error levels were included in the subsequent analyses.
(b) Principal Component Analysis (PCA)
Since shell character measurements are highly correlated, the morphometric data were analysed by PCA (Statistica for Windows Release 5.1, StatSoft Inc., 1996). The PCA maintained the morphological distances among species, yet removed the redundancy of highly correlated shell characteristics. Therefore the primary objective of using PCA was to summarise the variation from a correlated multi-attribute to a set of uncorrelated components.
The total suite of six shell character measurements was pre-examined for homogeneity and transformed to natural logarithms to enhance normality and equalize variances.
The proportion of the variance subsumed by each component was then expressed as an eigenvalue. This provided a series of loadings showing the correlation of the measured characters with the principal components (Blackith and Reyment, 1971; Kuris and Brody, 1976; Wellington and Kuris, 1983; Rohlf, 1996). The eigenvalues were then used to create a multivariate plot using forward stepwise discriminant function analysis.
(c) Discriminant Functions Analysis (DFA)
A discriminant functions analysis is an inferential analysis that maximises between-group variability and minimises within-group variability, thus allowing for a high percentage of correct groupings for conchologically similar species (Flury and Riedwyl, 1983; Norušis, 1990; Armbruster, 1995). The significance of the overall discriminatory power of the analysis was tested using the Wilks‟ Lambda standard statistic, while the standardised coefficients were studied to examine each shell character‟s contribution in the
discriminant function.
The analysis was performed using Statistica for Windows Release 5.1, Statsoft Inc., 1996. All assumptions required for the DFA to be performed were met. These were that no two morphometric characters should be highly correlated and that there was no significant deviation from normality.