Fluctuating Asymmetry of Plant Leaves: Batch Processing with LAMINA and Continuous Symmetry Measures

John Graham,Mattie Whitesell,Hagit Hel-Or,Mark Ii,Eviatar Nevo,Shmuel Raz

doi:10.3390/sym7010255

Abstract

Unlike landmark methods for estimating object asymmetry, continuous symmetry measures (CSM) can be used to measure the symmetry distance (ds) of inconsistent objects, such as plant leaves. Inconsistent objects have no homologous landmarks, no consistent topology, no quantitative consistency, and sometimes no matching points. When CSM is used in conjugation with LAMINA Leaf Shape Determination software, one can quickly and efficiently process a large number of scanned leaves. LAMINA automatically generates equally-spaced points around the perimeter of each leaf and the resulting x-y coordinates are normalized to average centroid size prior to estimating ds using a fold, average, unfold algorithm. We estimated shape asymmetry of leaves of three species of flowering plants: Ligustrum sinense (Chinese Privet), Rubus cuneifolius (blackberry), and Perilla frutescens (Perilla), as well as individual leaves from a few species of oaks (Quercus) and maples (Acer). We found that 100 to 200 equally-spaced points worked well for all three of the main species. Measurement error accounted for a small proportion of the asymmetry variation. Nevertheless, measurement error was great enough to generate some negative size scaling after normalization to average centroid size.

Highlights

Most plant leaves are inconsistent objects having no homologous landmarks, no consistent topology, no quantitative consistency, and few matching points [1]
We describe a high-throughput approach that can automatically measure the shape asymmetry of ten or more leaves in three steps
Most leaves have just two stable landmarks, which is insufficient to estimate shape. Because these landmarks are on the axis of mirror symmetry, they cannot be used by themselves to estimate shape asymmetry

Summary

Introduction

Most plant leaves are inconsistent objects having no homologous landmarks, no consistent topology, no quantitative consistency, and few matching points [1]. They pose numerous difficulties for biologists studying the fluctuating asymmetry (i.e., random deviations from perfect symmetry) of plants. The usual approach is to measure asymmetry of leaf width or vein length on right and left sides [2,3] These approaches only reflect linear dimensions and it is tedious to process one leaf at a time. We describe a high-throughput approach that can automatically measure the shape asymmetry of ten or more leaves in three steps This approach requires only a flatbed scanner, LAMINA (UmeåUniversity, Umeå, Sweden) software, and a MATLAB

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