## Introduction

The comparison of anatomical features of organisms, and understanding how variation in those features associates with variation in other traits, has long been of interest to ecologists and evolutionary biologists. In recent years, the quantitative study of anatomical form has matured into the field of morphometrics: the study of shape variation and its covariation with other variables (Bookstein 1991; Rohlf & Marcus 1993; Adams, Rohlf & Slice 2004; Zelditch *et al*. 2004; Adams, Rohlf & Slice 2013). One common approach to shape analysis, *geometric morphometrics* (GM), utilizes the coordinates of landmarks to record the relative positions of morphological points, boundary curves and surfaces as the basis of shape quantification. Geometric morphometric shape analyses are typically accomplished through a series of steps that can be called the Procrustes paradigm (Adams, Rohlf & Slice 2013). First, a set of two- or three-dimensional landmark coordinates are obtained on each specimen, which record the relative positions of anatomically-corresponding (or homologous) locations. Next, a generalized Procrustes analysis (GPA: Gower 1975; Rohlf & Slice 1990) is used to superimpose the specimens to a common coordinate system by holding constant variation in their position, size and orientation (an additional step is included to standardize points on curves and surfaces: Bookstein *et al*. 1999; Gunz, Mitteroecker & Bookstein 2005). From the Procrustes-aligned coordinates, a set of shape variables is obtained (Bookstein 1991; Dryden & Mardia 1998; Rohlf 1999), which can be used in multivariate statistical analyses to address a wide range of biological questions. Finally, graphical methods are used to visualize patterns of shape variation and facilitate descriptions of shape changes.

Because geometric morphometric methods provide a more comprehensive quantification of biological shape as compared to alternative approaches, their use in ecological and evolutionary studies has increased dramatically in recent years. For instance, geometric morphometric methods are now commonly used in studies of evolutionary quantitative genetics (Klingenberg, Debat & Roff 2010; Adams 2011; Martínez-Abadías *et al*. 2012), to reveal phenotypical changes associated with species interactions (Adams 2004; Langerhans *et al*. 2004; Adams, West & Collyer 2007), to describe patterns of fluctuating and directional asymmetry (Klingenberg, Barluenga & Meyer 2002; Schaefer *et al*. 2006), to identify convergent and parallel evolution (Stayton 2006; Adams 2010; Adams & Nistri 2010; Piras *et al*. 2010), to discover phylogenetic and macroevolutionary trends (Sidlauskas 2008; Klingenberg & Gidaszewski 2010; Monteiro & Nogueira 2011) and to reveal ontogenetic patterns in human evolution (Bookstein *et al*. 2003; Mitteroecker *et al*. 2004; Mitteroecker & Bookstein 2008), among other applications. Consequently, several software packages are now available for applying geometric morphometrics to particular problems. However, freely available software implementing all of the steps of the Procrustes paradigm in a single computer package, including the digitization of specimens and the analysis of both fixed landmarks and sliding semilandmarks in two- and three-dimensions, is generally lacking.

The purpose of geomorph is to fill this gap. Geomorph (Adams & Otárola-Castillo 2012) is a freely available software package for performing geometric morphometric shape analysis in the r statistical computing environment. It can be installed from the Comprehensive r Archive Network, CRAN. In geomorph, routines for all stages of landmark-based geometric morphometric analyses are provided, including: digitizing landmarks on two and three-dimensional objects; reading and manipulated landmark data files; generating shape variables via Procrustes analysis for points, curves and surfaces; performing statistical analyses of shape variation and covariation; and providing graphical depictions of shapes and patterns of shape variation. A variety of statistical methods for shape analyses germane to ecological and evolutionary studies are included. Geomorph extends the capabilities of landmark-based shape analysis in r over prior packages and routines (e.g. the ‘shapes’ package: Dryden 2012 and *Morphometrics With *r: Claude 2008), by incorporating both semilandmark methods and the digitization of specimens directly within r. However, because geomorph utilizes previously developed data structures implemented in these packages, one may combine functions across packages to expand the breadth of shape analyses available within the r computing environment. Below we describe some of the major features of geomorph to demonstrate some of its functionalities.