Here is a paper on this problematic which may help you.

http://www.italian-journal-of-mammalogy.it/Missing-the-third-dimension-in-geometric-morphometrics-how-to-assess-if-2D-images,77196,0,2.html

Here is a paper on this problematic which may help you.

http://www.italian-journal-of-mammalogy.it/Missing-the-third-dimension-in-geometric-morphometrics-how-to-assess-if-2D-images,77196,0,2.html

Dear Susan,

The paper recommended by Dimitri is a good one. And there you will find a good explanation on how studying 3D structures by means of 2D images can affect your conclusions regarding morphological variation. However, I think that your question is more specific and oriented to a particular objective. If I have understood properly you wish to know if a given set of measures taken on 2D images will be useful to assign specimens to a particular species. I am affraid that the answer is that it will depend on several aspects. One of them is the specific set of measures. If the traits are mainly oriented in the plane of the picture, the measures will not be severely affected by taking the measure in a 2D image. I would avoid measures that take points at different planes in a given picture (because they will be more affected by orientation and the projection of the third dimension on the 2D image). Other aspect is how are the photographs taken. It would be important to take the photographs with same conditions as much as possible (distance to the object, zoom, angle...). In my opinion if the set of photographs and the set of measures are obtained taking these aspects into consideration, obtaining the measures from 2D images should not seriously affect the allocation of the specimens to a particular species. In fact, your capacity to assign specimens to a particular species will depend on the "true" variation among them, and the capacity to detect this variation. Which in turn will depend on the noise (error) that your measurement methods will inevitably add.

I hope this will help.

Francesc

Thank you Dimitri and Fransesc for your useful answers and the paper recommendation - it is definitely a good source!

To clarify: My data are not distances from pictures but actual 2D distance measurements taken with a caliper from real skulls and therefore not limited to the constraints of photographic images.

But - especially over long distances and whenever the distance between two points is not straight but curved (e.g. length of skull can be measured as total straight length or length over the curved top of the skull) the real 3D nature of that specific distance is not 100% correct.

To frame my question more specifically and collect further input of the limitations of my measurements:

What specific, important, (potentially species-defining) information could be contained in a 3D scan that is definitely not displayed in a 2D distance?

Thank your for providing feedback!

Dear Susann,

Ok. Then, you work with linear measurements but taken in a "3D space" (the real space). In my oppinion, in such a situation the issue is not only the dimensionality of the data, but which data you will analyse and which methodology you will use to do it. I mean, you could construct 3D models of your turtles and obtain the same set of linear measuremets that you are now recording on true animals. The measures could be more precise (or not), but you would be working with the same type of data: linear measures (obtained from a 3D -real or virtual- object). The multivariate statistical analysis of linear measurements (such as yours) is usually called traditional morphometrics. A more recent focus is not working with linear measures but with the coordinates of anatomical points called landmarks. This methodological focus is called geometric morphometrics. Geometric morphometrics has proved to have several advantages over traditional morphometrics. One of them is that form can be decomposed into size and shape, which can be analysed separately (this is interesting because they can have different biological meanings). Another advantage is that, usually, with the study of the displacements of landmarks, precise information on small changes of form can be captured. These changes would probably not be captured with a traditional set of measures. Of course, this does not invalidates using linear measures. In addition, when anlysing form by means of geometric morphometrics you can do it in a 2D or 3D space. When analysing form changes with a strong 3D component (such as a turtle) the second option is preferable because working in 2D implies a loss of information and the projection of form variation in the third dimension onto the other two dimensions.

Hope this will help.

Francesc

The orientation of structures relative to each other and the configuration of structures within 3D space cannot be captured from 2D data. You may have two turtle species that have skulls that are of equal length and equal width at different locations, but these points are arranged differently relative to each other in the real specimen. Numerically they would look the same, but in reality they would not. Often these might be more important differences than simple 'size' differences. Of course it depends on the organism and the measurements.

One way to get around this is to use photographs to calculate angles between structures, albeit imperfectly (compared to 3D methods). Another way could be to collect 'extra' measurements that capture the missing distance between points in all three dimensions. For example, if you are doing anterior and posterior widths of the skull as measured from a superior view, also collect the distance between the anterior and posterior width, and between each of the widths and additional landmarks on the skull, for example a landmark on the inferior of the skull. Again this is imperfect and laborious compared to 3D methods but may help you capture extra information that is more easily obtainable with standard instruments such as calipers or photos.

In terms of differentiating species you could also include non-measurement characters such as which bones form sutures, number of teeth, etc. if those are relevant to turtles.

Linear measurements still have a place morphometrics. They are faster to collect, require less specialized equipment, and they facilitate easy comparison with previously collected datasets. Of course, if the equipment is available to collect 3d landmarks, e.g., with a mircroscribe or landmarks on ldigital 3d models, then you can derive linear dimensions from the landmark coordinates (facilitating direct comparison with other datasets) AND have the opportunity to study 3D relationships, including between points that you didn't originally intend to compare.

Hi Susann, in my opinion 2D linear morphometrics are a perfectly good source of valid morphological data. Here's another good example: Article What is Panthera palaeosinensis?