From shapes to numbers, and back again

Why do organisms have different shapes? The morphology of species is not random, but the result of a long process of evolution and adaptations to the species’ environment and behaviours. Fish show a large diversity in shapes (e.g. flat fish, eel-like, torpedo-shaped), but how to measure such a diversity? In other words, how to compare objectively the shapes of fish found across an ecological gradient? Those are the questions that Caillon and coauthors tried to answer in a study recently published in Ecosphere (DOI 10.1002/ecs2.2220).

Figure 1
Figure 1: Extract from "On growth and form" by D'Arcy Thompson, scientist known to be the first biomathematician.

We all know how to recognise and compare shapes visually. In fact, we do it constantly in our everyday life. But it is harder to measure and quantify the differences between shapes. Shape is defined here as all information which is not due to differences in rotation, size or position. Three main approaches were developed to measure and compare shapes: traditional morphometrics, geometric morphometrics and outline analysis. Let’s illustrate the differences with an example: Atlantic cod (Gadus morhua), an iconic species that is both heavily fished and studied (e.g. see recent blog posts about the recent collapse of cod, the spawning migration and the genetic description of Northeast Arctic cod).

Figure 2: Comparison of morphometric methods
Figure 2: Comparison of morphometric methods

Traditional morphometrics rely upon the measurements of shape indicators such as length, area, angle, and their ratios (Figure 2a). The focus is on selected aspects of shape, which are known to be linked with functions (e.g. feeding or swimming). However, the original shape cannot be reconstructed from the measured indicators and information about the original shape is lost. Modern morphometrics were developed in the late 80’s to overcome this issue (Rolhf and Marcus 1993) and two main methods are equally popular: geometric morphometrics and outline analysis. Geometric morphometrics use homologous points between shapes, known as landmarks, and studies their relative position (Figure 2b). However, the selection of homologous points is subjective and difficult to define for shapes from distant families.

The third approach, outline analysis, considers the coordinates (i.e. the x and y positions) of the whole outline of the shape (Figure 2c). The most popular outline analysis is elliptical Fourier transforms (EFT), and it has already been used in marine biology (e.g. to describe otolith shapes). EFT transforms the x and y coordinates of the outline into periodic functions (Figure 3a). These functions are decomposed mathematically as a sum of sine and cosine functions (called Fourier transform, see Bonhomme et al. 2014 for more details). The algorithm estimates the best ellipse (called first harmonic) that would fit the shape (Figure 3b). Then, it uses a second ellipse (i.e. second harmonic) rotating twice along first ellipse, that refines the numerical description of shape. The process continues until the shape is fully described by the successive harmonics (Figure 3b). Using this method, we can compare the morphology of organisms from distant families, such as species assemblages in a diverse ecosystem.

Figure 3: Illustration of outline analysis on Atlantic cod.

Our recent study (Caillon et al. 2018) shows that outline analysis is an efficient way to measure the morphological diversity of a fish community. We used 218 images of 85 species that inhabit the North Sea and linked their morphological characteristics to their spatial distribution. We found a significant difference in morphological diversity across a strong ecological gradient in the North Sea. The southern North Sea, characterised by shallow and highly productive waters showed higher morphological diversity compared to the northern North Sea which is deeper and have lower seasonal variation in the bottom water. The outcome of the outline analysis can be of great interest for further trait-based approaches in ecology and biogeography.

So, are you ready for a morphometric dive into fish diversity? Check out our paper here ( or you can find a tutorial explaining our analysis at:



Bonhomme, V., Picq S., Gaucherel C., & Claude J. (2014). Momocs : Outline Analysis Using R. Journal of Statistical Software 56:1–24.
Caillon F., Bonhomme V., Möllmann C. & Frelat R. (2018) A morphometrics dive into fish morphology, Ecosphere, 9(5):e02220.
Rohlf F. J., & Marcus L. F. (1993). A revolution morphometrics. Trends in Ecology & Evolution, 8(4), 129-132.

Tags: morphology, fish diversity, modern morphometrics, biomathematics By Romain Frelat, edited by Esther Beukhof, Florian Caillon and Tin-Yu Lai
Published June 4, 2018 8:38 AM - Last modified June 4, 2018 8:38 AM