Size and shape—integration of morphometrics, mathematical modelling, developmental and evolutionary biology

Abstract

The German philosopher Arthur Schopenhauer (1788-1860) once said: "Any foolish boy can crush a beetle with his foot, but all the professors in the world cannot make a beetle". This quote summarizes the limited knowledge in the midnineteenth century about the mechanisms that generate a new individual. But, it still reflects our limited knowledge of the genetic control of morphogenesis. Studies in a number of model systems, especially in the fruit fly Drosophila melanogaster, have revealed basic principles of how the body axis, segments or organs like the wing are specified, for example. However, we are still lacking a comprehensive understanding of how organisms and their organs know when to stop growing or how to attain their final shape, which is often species specific or even specific to an individual. The basis of size: cell size and cell numbersIn theory, the size of an organ can mainly be changed in two ways: either by changing the size of the individual cells or by changing the number of cells, and thus, an understanding of size control should be possible by studying the mechanisms of cell growth and cell proliferation.In practice, however, the control of cell number and cell size is more complex. For each process, there are several cellular mechanisms. For instance, cell number can be determined not only by controlling the production of new cells but also by killing cells that were already produced (cell death). Thus, positive and negative regulatory mechanisms of cell growth and cell number complement each other. In addition, there is evidence that the mechanisms that control cell growth and those that control cell number can communicate and influence each other. Diploid and tetraploid salamanders, for instance, develop organs of comparable size although in the tetraploid animals, the cells are much larger. The organs compensate for the bigger cell size by reducing the number of cells (Fankhauser 1952). Similarly, a decrease in cell number in plant mutants is associated with an increase in cell size and vice versa. This compensation ensures that despite alterations during development, functional leaves are formed (Gonzalez et al. 2012). Size control: autonomous vs. non-autonomousIn the early 1920s, Harrison and later also Twitty and Schwind transplanted organ anlagen of salamander legs and eyes from a small species into a large species and vice versa. Intriguingly, the size of the transplanted organs always resembled the size in the source species rather than the new host. Thus, the information about their final size must have resided within the transplanted legs and eyes themselves (Harrison 1924; Communicated by Nico Posnien and Nikola-Michael Prpic

Scan, extract, wrap, compute—a 3D method to analyse morphological shape differences

“…This facilitates evaluation of morphological alterations, e.g., in an ecological context as it is appropriate in our case study. Alternatively, studies on knock-outs of, for example, Drosophila or zebrafish embryos, may aim to detect just such size differences in detail ( Prpic & Posnien, 2016 , and references therein). Thus, the size-adjustment during Procrustes analysis needs to be performed depending on the questions asked in the respective study.…”

The genetic control of leaf and petal allometric variations in Arabidopsis thaliana

“…To address this question, some quantitative genetic frameworks have been built up to quantify organ shape and size [1,3,[10][11][12]. With these frameworks both the size and shape differences are measured and compared to resolve the allometry variance between different organs.…”

The genetic control of leaf and petal allometric variations in Arabidopsis thaliana

“…Shape, on the other hand, is a much more complex feature, and it is far more di cult to measure and compare. In the 1980s, advances in the development of statistical analytic tools and their combination with outline and landmark data revolutionized the eld of geometric morphometrics (Prpic and Posnien, 2016). A point and outline approach was rst ampli ed to quantify allometric variation within the leaves of the snapdragon (Antirrhinum) species (Langlade et al, 2005).…”