Background

Morphology has long been recognized as a fundamental trait in the field of biology. The intricate relationship between morphogenetic and evolutionary factors, as well as morphospaces, underscores the need for multivariate methods in biological and ecological research [1]. Geometric morphometrics (GM) has emerged as a widely utilized approach for the quantitative analysis of shape variation, particularly in the domains of biology and anthropology. It has become one of the primary methods for assessing essential morphological variables because it provides a quantitative/unbiased approach and morphological comparison [2]. GM has been instrumental in addressing a diverse array of questions related to morphological variation, including population differences, developmental patterns, responses to environmental factors, evolutionary trends, and functional morphology. Within the realm of morphology, three styles of morphometrics are commonly employed: traditional morphometrics, landmark-based GM, and outline-based GM [3]. In general, GM encompasses the following analytical steps: data acquisition, morphological variation analysis, results visualization, and interpretation.

For novice practitioners, the intricacy of GM often arises from the complexities associated with data construction and transformation, as well as the diverse array of analyzing methods available. Throughout the process, landmarks serve as the foundation for quantifying shape. GM analysis can be conducted using distinct landmark configurations for landmarks and semi-landmarks [4]. Traditionally, there are three types of landmarks [5]. However, as GM has advanced, the classification system for landmarks has evolved, with a more convenient typology being utilized in applied studies [6,7]. In the updated typology, the conventional roster of landmark points can be categorized into six types, intended to supersede the three types outlined in Bookstein [5]. This new classification corresponds to the different operational origins of the points along the curve or curves on which they are situated [6]. The process of landmarking and classifying landmarks may heavily rely on biological interpretation, and the major limitation of these types of techniques is that the labeling-analysis processes are all semi-manual or manual. Nevertheless, landmarking analysis remains the primary technique used in GM to this day. The characteristics of landmarks are described below.

1. Type I landmarks (anatomical landmarks)

   1. Definition:

      1. Points of clear biological or anatomical significance that can be precisely and consistently identified across all specimens.

      2. These landmarks correspond to specific, discrete, and easily recognizable anatomical features.

   2. Examples:

      1. The tip of the nose.

      2. The corner of the eye.

      3. The junction between bones.

   3. Advantages:

      1. High reliability and repeatability.

      2. Easily comparable across specimens due to clear homology.

   4. Applications:

      1. Frequently used in studies of skeletal morphology and other well-defined anatomical structures.

2. Type II landmarks (mathematical landmarks)

   1. Definition:

      1. Points defined by geometric properties such as maxima or minima of curvature, or points where certain geometric properties change.

      2. These landmarks may not correspond to specific anatomical features but are identified based on their geometric properties.

   2. Examples:

      1. The point of maximum curvature along a bone.

      2. The deepest point in a notch.

   3. Advantages:

      1. Useful for capturing shape information where anatomical landmarks are not clearly defined.

      2. Can provide additional geometric context to the shape.

   4. Applications:

      1. Often used in conjunction with Type I landmarks to provide a more comprehensive shape analysis.

3. Type III landmarks (constructed landmarks)

   1. Definition:

      1. Points defined by their relative position or constructed based on other landmarks.

      2. These landmarks are not associated with specific anatomical features but are placed based on their geometric relationship to other landmarks.

   2. Examples:

      1. The midpoint between two anatomical landmarks.

      2. Points evenly spaced along a curve or surface.

   3. Advantages:

      1. Flexible and can be used to outline complex shapes.

      2. Useful in capturing the overall geometry of a structure.

   4. Applications:

      1. Frequently used in semi-landmark analysis to capture the shape of curves and surfaces where fixed landmarks are insufficient.

         Procrustes superimposition serves as the foundational step for subsequent analysis in GM [8]. Biologists have grappled with aligning the method of "Cartesian transformations" and "transformation grid" with geometric patterns since its original exposition [9]. Three decades ago, the concept of "morphometric synthesis" emerged, combining Procrustes shape coordinates with thin-plate spline (TPS) renderings for various multivariate statistical comparisons [10]. However, a concluding discussion suggests that the current toolkit of GM, centered on Procrustes shape coordinates and TPS, may be too limited to accommodate the interpretive needs of evolutionary and developmental biology [11]. Common methods used to identify major modes of shape variation and determine group differences include principal component analysis (PCA), TPS, discriminant function analysis (DFA), partial least squares (PLS), and canonical variate analysis (CVA). The interpretation of these methods is based on biological questions or hypotheses, combining patterns of shape variation, key landmarks or curves, and findings with relevant evolutionary or ecological factors.

         GM has experienced a surge in applications within evolutionary biology and ecology, particularly with the use of three-dimensional imaging data [12]. However, the majority of studies involving fish morphology are based on two-dimensional data. GM analysis in fisheries primarily focuses on species taxonomy, group diversity, individual development and evolution, and ecomorphological variation [13]. The development of software and the reduction of technical limitations in analysis may enhance fish research. GM has evolved alongside advancements in theory and technology, resulting in a variety of software and analysis methods. There are large pre-existing datasets of fish images that can be analyzed using appropriate GM methods. However, several analysis techniques are often required for a single research project, which can present challenges for novices. Consequently, this protocol aims to compile a comprehensive set of methods for conducting GM analysis on fish using two-dimensional data. Although there are no established standards for performing GM analysis, advancements in technology are crucial for characterizing variations in fish body shape. Furthermore, it is anticipated that this approach will facilitate the sharing of morphological data and help resolve related scientific problems. [14], potentially expediting scientific advancements in the field of fish biology and ecology [15].