**Hethke, M., Hartmann, K., Alberti, M., Kutzner, T. &
Schwentner, M. (2023). Testing the success of palaeontological methods
in the delimitation of clam shrimp (Crustacea, Branchiopoda) on extant
species. Palaeontology, 66, e12634. doi:10.1111/pala.12634**

Hethke et al.Â (2023) applied Linear discriminant analysis (LDA) to evaluate whether morphological distinction through carapace traits (size, shape, ornamentation) adequately reflects species discrimination among clam shrimp.

The hypotheses regarding size and shape (ornamentation not covered here) are:

*H1. Size and shape are informative for the discrimination of
Ozestheria species.*

*H1a: Species are morphologically distinct (separate analyses of
size and shape).*

*H1b: The combination of size and shape variables leads to higher
accuracies in species discrimination than analyzing each
separately.*

All Data and R-markdown files for this study are available in the Dryad Digital Repository and can be downloaded here.

Here, only a brief summary of selected parts of the analysis are presented.

A total of 481 specimens from ten different *Ozestheria*
(sub-)species were selected from a larger dataset collected in Australia
(Schwentner et al.,
2015). Each individual was photographed and the carapaces outlined
and measured using a vector graphics program. The nine different linear
measurements describing each carapace can be seen in the figure
below:

The size variables were standardized by dividing each measurement by the arithmetic mean of all nine measurements. Values were then transformed into the real space by using the natural logarithm. The shape parameter was determined using a Fourier shape analysis.

The data analyses for H1a included a linear discriminant analysis (LDA) of the size and shape datasets. For each of the 45 pairwise species combinations samples of individuals with predefined species identity were randomly selected (training set).

The linear discriminant models were implemented in R using the
`lda()`

function from the `MASS`

package. The
corresponding species served as the grouping factor and the size and
shape parameters as the covariates. LDA provides a method to find the
linear combination of covariates, which best separates the species
groups.

Next, the developed models were used to classify individuals with
unspecified species identity (test set) using the `predict()`

function. Model performance was assessed by iterating the sampling and
modeling steps 300 times and calculating the mean number of correctly
classified individuals. This mean accuracy also allowed to measure
morphological separation between species pairs.

In addition to the separate data analyses for H1a, the linear measures (size) and Fourier coefficients (shape) were combined and the same methodology applied for H1b. For this analysis one species (C) was excluded since it strongly differed morphologically from the remaining species.

The overall mean accuracy of the LDA test results over all species combinations is around 93 % (for size and shape). The mean accuracies between the species pairs differ between <80 % to 100 %. Among the pairs with the lowest classification accuracy based on size parameters are two combinations of sister species. While for most species pair comparisons the accuracy is higher based on shape than based on size, the opposite is true for some species pairs.

The overall mean accuracy of the combined analysis of size and shape is slightly higher than for the separate analyses. In addition, the results show that each of the genetically differentiated species is morphologically distinct. Still, when strongly differentiable species C is excluded, the remaining nine species are closely positioned in the morphospace: