The Nutty Professor 2

Drug control is one of the more messy fields of integration of science and policy, and is certainly up there with climate change and the mechanics of Boris Johnson’s hair. The post from yesterday demonstrated how complex the science-policy interface can be, with respect to David Nutt’s dismissal from the Advisory Council on the Misuse of Drugs after pushing for his evidence to be used to guide policy reform in drugs control. Throughout, I made the assumption that his science was rigorous enough, not to avoid challenge, but to at least be of value to policy and decision-making processes. My current commute to and from Leicester is mind-numbingly boring. To offset this, on the way home I read his infamous co-authored paper from 2009, published in The Lancet for an analysis conducted into the relative harms of drugs in the UK. What I read about was a series of poorly-conducted analyses, and statements that didn’t seem to fit their results or were vague, meaningless and unsupported.

Another Page Written in the History of Tetrapod Biodiversity

The story of vertebrate evolution over the last 250 million years is one of the most remarkable, and most complex to unravel, stories of all time. Throughout the ages, extraordinary species and groups have come and gone, and we are left now with only a fingerprint of times long forgotten. Recreating and detecting macroevolutionary patterns within and between vertebrate groups using the fossil record involves an excruciating amount of work, due to the massive amount of data required to be sampled, and the potential number of parameters that could influence biological trends.

Continuing work from his MSc thesis, Roland Sookias (and Roger Benson and Richard Butler) continues to make a name for himself by rigorously analysing the terrestrial tetrapod record within the late Palaeozoic and early Mesozoic. His latest paper [free to access!] extends the analysis of his first (looking at the interaction of intrinsic traits (i.e., body mass) within and between clades of tetrapods around the time that dinosaurs began their ascent) by looking at the impact of extrinsic (i.e., environmental) parameters on body size.

Did Archaeopteryx Really Have Black Plumage?

Not surprisingly, the latest Archaeopteryx study has kicked up quite a stir within the media and scientific realms, considering the iconic status it has attained since discovery some 150 years past. This latest paper by Carney et al. and published in the journal Nature Communications claims to have resolved the plumage colour of a feather possibly from  Archaeopteryx, a pretty neat little addition to the reconstruction of this critical species. They use methods employed during previous studies, namely the morphological or structural analysis of melanin-bearing organelles within feathers called melanosomes to infer that Archaeopteryx possessed an entirely black plumage.

The notorious black feather (Image Copyright: WitmerLab at Ohio University)

There is no doubt that the structures are in fact melanosomes, and no doubt that melanosomes contribute to plumage colour. But the question is, how much do they contribute to the plumage colour..? Well, I don’t know. In fact, no-one knows, at least in extinct avian theropods. The authors don’t discuss this either. It has however been discussed elsewhere in similar studies, albeit only qualitatively and in passing.

One comment is from Zhang et al. 2010: “Melanosomes are lyosome-related organelles of pigment cells in which melanins are stored and are responsible in part for the colours exhibited by modern birds.”

And Li et al. 2010: “Other molecular pigments such as carotenoids and porphyrins also produce plumage colours but are not preserved morphologically, thus we cannot address their possible effects here.”

That seems like a pretty big caveat. It’s like saying if you mix green, yellow and red paint in unknown quantities, you get red every time. Or something similar, I suck at analogies. The point is, if in modern birds, there are other significant structures that dictate or contribute towards plumage colour, does it make sense to try and predict colour when these are absent?

UPDATE: Ryan has been kind enough to clarify this point in a comment below.

Furthermore, the 95% confidence intervals the authors use are practically useless. Look at the ordination provided in Figure 4 (not sure if I can copy it here, so won’t..).  These 95% confidence ellipses mean nothing in the slightest, or at least nothing meaningful. What they should have shown is an envelope includes 95% of all points within a sample, so that when you insert data ‘blind’, if it falls within a completely discriminated envelope, you can be 95% certain that it belongs to that group (i.e., 95 times out of 100, a blind data point will be correct). The envelopes shown in figure 4 clearly do not show this (if you don’t have access to the paper, ask me for a copy, or take my word for it). As a result, the points calculated for the particular Archaeopteryx feather analysed could really be grey or black, or maybe brown at a push (the number of colour choices is simply overwhelming..).

So was Archaeopteryx lithographica black?

Probably, probably not.

Carney et al. (2012) New evidence on the colour and nature of the isolated Archaeopteryx feather, Nature, DOI: 10.1038/ncomms1642

Li et al. (2010) Plumage patterns of an extinct dinosaur, Science, 327, 1369-1372

Negro et al. (2009) Porphyrins and pheomelanins contribute to the reddish juvenal plumage of black-shouldered kites, Comparative Biochemistry and Physiology Part B: Biochemistry and Molecular Biology, 153(3), 296-299

Zhang et al. (2010) Fossilized melanosomes and the colour of Cretaceous dinosaurs and birds, Nature, 463, 1075-1078

Quantitative Shape Analysis 2: Data Collection – easier than you think!

“If you want to inspire confidence, give plenty of statistics. It does not matter that they should be accurate, or even intelligible, as long as there is enough of them.” Lewis Carroll (1832-1898)

 

The last post on this series gave an introduction to the background and significance of quantitative shape analysis. I conveyed the use of landmarks, or geometric co-ordinates, as the basis for statistical analysis of shape. The last article finished by stating this article would discuss different methods of geometric morphometric analysis, but I forgot one crucial step: Data Collection! Here, I present a simple and efficient way of collecting data for use as the basis for a range of geometric morphometric analyses.

Following is an example of data collection from a simple coursework study I did last year, looking at cranial allometry in carnivores. Firstly, you need a target or hypothesis for your analysis. The target here was to use exemplar carnivorous mammal species to look at shape variation in the skull, and to interpret in terms of form and dietary function. The first decision to make is what points to use as your landmark data. I’ll use a hypothetical skull as an example.

Chosen selection of landmarks - you can chose any, as long as they are topographically correspondent between all specimens as described in the last post

 

Each one of these landmarks represents a specific topographically correspondent point amongst all specimens in the sample. For the sake of simplicity in this example, assume that the lower jaw and the cranium are a single module. The landmarks can be defined as such:

Cranial landmarks (right-lateral aspect; red)

1. Posterior extremity of occipital margin (type 3)

2. Tympanic aperture (centre) (type 1)

3. Posteroventral extremity of occipital condyle (type 3)

4. Ventral extremity of dorsal postorbital process (type 3)

5. Rostral extremity of orbital periphery (type 3)

6. Mid-point on ventral maxillary margin between premolars and canines (type 3)

7. Ventral deflection in dorsal margin (maximum curvature) [rostral to postorbital] (type 2)

8. Dorsal expansion in dorsal margin (maximum curvature) [posterior to external nares] (type 2)

9. Anterior extremity of premaxilla (type 3)

10. Dorsal extremity of dorsal margin (type 3)

11. Ventral extremity of zygamatic arch-jugal suture (type 1)

12. Position of distal border on posterior-most tooth (maxillary) (type 1)

 

Lower jaw landmarks (right-lateral aspect; blue)

13. Posterior extremity of angular process (type 3)

14. Posterior-most (distal) extent of dentary molars (type 3)

15. Mid-point on ventral dentary margin between premolars and canines (type 3)

16. Anterior extremity of dentary (type 3)

17. Point of posterodorsal deflection of ventral margin, culminating in angular process (type 2)

18. Ventral pinnacle of coronoid process (dentary) (type 2)

 

This is just a hypothetical example to show landmark positions and how to define them. Real data is freely available for almost anything on the internet. A series of sample images can be easily obtained through MorphBank, for example. If anyone reading this would like, I can send them a copy of the images I used for this coursework as a trial data set – just drop me a quick message with your email address.

Converting these landmarks into usable geometric data is possible through a number of image modification programs. A good one to use is ImageJ, freely available on the web. An important thing to note at this point is that within your image collection, every one you import into this program or any other must be angularly identical, or as close as possible (e.g., all of a precise lateral view of a skull).

Using ImageJ you can simply import an image with pre-defined landmarks as above, use the ‘Point’ tool to click on the landmark, hit ctrl-m (or use the Analyse-Measure tab), and hey-presto, you have the two-dimensional geometric co-ordinate of that point in a table! Consecutive points can then be added to this table for each specimen. Do this for all points per sample in a pre-defined numerical sequence (as indicated above), then simply export to an Excel spread-sheet. A rather nifty thing you can then do is plot them as a graph, and you’ll see a landmark representation of your image (awesomeness of this depends on how many landmarks you use). Repeat for all samples, and you have a comparable data set. Simple eh! Note that this can be done free of scale, so you don’t need to measure any lengths or inter-landmark distances. A future post will cover how to compensate for this in quantitative shape analysis. What you want to end up with at this stage is a single spread-sheet, with a labelled tab for each specimen, and containing a series of geometric co-ordinates that are topographically related between specimens.

There are of course more techniques using more complex software and data imaging methods (using surface or outline data, laser scans etc.), but typically these will not be accessible to the general public. The above procedure is a convenient and free method of obtaining a decent and workable initial data set, without having to spend endless time in a museum collection or laboratory.

So, now you know the procedure, nothing should stop anyone from going out there and collecting a data set, constructing a series of landmarks and digitally obtaining their geometric co-ordinates. Right? Next time, I’ll actually discuss how to assemble this data into a format that you can use to input to some free software, and several analyses you can then conduct with this software (e.g., Principal Components Analysis).

Why Geometric Morphometrics Kicks Ass 1

Those of you who have read my recent articles will probably have noticed the phrase ‘geometric morphometrics’ a few times. When mentioned to people, the usual reaction is to melt or run away screaming satanic verse and tearing chunks of hair out (pers. obs). This is largely due to the pretty intense mathematical basis behind the huge variety of implementable statistical procedures, which range from simple linear regressions to more complex 3D extended-eigensurface analyses. Each of these essentially provides a quantitative method of analysis of biological structures that can be interpreted in terms of biological function, a pretty crucial aspect of both zoology and palaeontology. To get to grips with the necessary analytical tools, it’s not really important to dig into the fundamentals such as how to construct a covariance matrix – these are well-defined mathematical concepts. The aim of the following few posts is to break down what is one of the most powerful yet under-used tools available for bio-structural analysis. What I’d also like to achieve is some kind of informal discussion about ideas in which geometric morphometrics can be applied to simple ‘pilot’ analyses based on freely available information, such as photographs from Morphbank. This first post will deal with the initial concepts, and future articles will provide examples of the different methods and tools available. Hopefully you will find this useful, and begin to openly develop and understand the processes involved.

Geometric morphometrics, as you might infer from the name, is the statistical analysis of form using geometric co-ordinates, or Cartesian landmarks. Form is defined here as the total dimensionality resulting from both shape and size. Size is the totality of spatial dimensions within a form, and shape is defined as the aspect of a form’s geometry that remains after scale (i.e., size), position (translation) and rotation have been normalised. Shape is essentially a localised metric for describing variation of spatial dimensions. Distinguishing between these is actually pretty crucial, as typically in an analysis you will want to differentiate between size and shape. Recently, the field has accelerated in strength due to the ability obtain three-dimensional structures such as skulls using techniques such as computer-tomography (CT) scanning. This considerably increases the information available for geometric morphometricians, and has led to numerous concurrent methodological adaptations in order to rigorously process available data. Using 3D techniques is kind of like a ‘total evidence’ approach to form analysis.

My personal opinion is that geometric morphometrics completely out-strips traditional morphometrics in terms of theoretical strength, methodology, and explanatory power. Consider simple linear measurements for starters, in for example, describing a lateral view of any mammalian hind-limb. You can imagine all sorts of bisecting, parallel, oblique and orthogonal measurements that would aid reconstruction of the form. Collecting these measurements and the relative angles would be time-consuming however, especially if you were looking for example, at sexual dimorphism of the femoral head in an antelope population. The world’s supply of coffee would be extinct before completion. However, with a simple photograph and the right software, breaking down a femur into a geometric outline or surface that you can use for all sorts of morphometric wizardry takes seconds (not including the months it takes until you are granted access to specimens).

Ratios are also a statistical over-simplification. The combination of measurements that can produce the same ratio is constrained only by the size of an object, and furthermore, ratios are a gross under-estimate of the potential geometric complexity of an object; try and imagine modelling a sine-wave with a linear ratio (or as complex a morphological structure as you want). Not going to happen is it.

The core of geometric morphometrics revolves around the assessment of allometry. Allometry is an ubiquitous aspect of nature, describing how organisms change their form. Discovering and interpreting allometry is the proximate target of most investigations, with the null hypothesis being isometry: no shape variation with respect to size. Typical investigable targets include detection of heterochronic trends, called paedomorphosis or peramorphosis, relating to the timing of acquisition of certain structures in an organism’s or species’ history (essential for evo-devo analyses).

Landmarks form the principal units of analysis for geometric morphometrics. Landmarks are formally known as Bookstein shape co-ordinates, with a defined Cartesian geometric position (i.e., x, y, z variables). Landmarks represent a subset of possible locations or distances, based on the nature of sampling. The only problems with this approach include difficulties in recognising landmarks, missing data, and possible redundance of data due to over-lapping inter-landmark spacings.

The data coverage available through morphometrics is exquisite! Each point is an individual landmark

REALLY IMPORTANT: Landmarks are NOT homologous sensu stricto. They represent topographically correspondent ‘characters’ – you should be able to write down the exact location in an unambiguous manner. This is really important when it comes to the biological interpretation of data.

There are three types of Cartesian landmark. Although not necessarily that important, it can provide an idea of how geometrically faithful a representation of an object you have.

Type 1: These represent the juxtaposition of biological components, such as sutures.

Type 2: These represent geometric aspects of form, such as local maxima or minima of curvature. These and type 1 landmarks are typically used in structure-based analyses.

Type 3: These are co-ordinate dependant equidistant interpolations, such as mid-points between two type 1 landmarks. They are also known as semi-landmarks, and are typically used in refining shapes such as profile outlines.

Landmarks form the cornerstone of all geometric morphometric analyses. What they provide you with is an unambiguous and quantitative dataset, that most importantly is highly informative in terms of biological structure. With landmark data, the wealth of potential modes of analysis at your disposal is phenomenal, as are the available software packages. One I would highly recommend is the tps series that can be found here, as well as a rather comprehensive overview of all things geometric.

In the mean-time, I wish everyone here an awesome 2012, and try not to get apocalypsed/raptured. I’ve popped a few references at the bottom here regarding the recent application of morphometrics in the field of vertebrate zoology, definitely worth reading a few just to get to grips with how scientists are currently using the techniques. I also strongly recommend the PalaeoMath series by Norm MacLeod, freely available here through the Palaeontological Association. It’s good stuff, and includes data so you can try your own analyses!

Next time: Principal Components Analysis, Principal Co-ordinates Analysis, and Procrustes superimposition.

Barden, H. E. and Maidment, S. C. R. (2011) Evidence for sexual dimorphism in the stegosaurian dinosaur Kentrosaurus aethiopicus from the Upper Triassic of Tanzania, Journal of Vertebrate Palaeontology, 31(3), 641-651

Brusatte et al. (2011) The evolution of cranial form and function in theropod dinosaurs: insights from geometric morphometrics, Journal of Evolutionary Biology, DOI: 10.1111/j.1420-9101.2011.02427.x

Goswami, A., Milne, N. and Wroe, S. (2010) Biting through constraints: cranial morphology, disparity and convergence across living and fossil carnivorous mammals, Proceedings of the Royal Society B, doi:10.1098/rspb.2010.2031

Hadley, C., Milne, N. and Schmitt, L. H. (2009) A three-dimensional geometric morphometric analysis of variation in cranial size and shape in tammar wallaby (Macropus eugenii) populations, Australian Journal of Zoology, 57, 337-345