Morphospace Approaches to Evolu�on:Geometric and Developmental Considera�ons
Dr. Sylvain GerberIns�tut de Systéma�que, Evolu�on, Biodiversité (ISYEB), Muséum na�onal
d'Histoire naturelle,CNRS, SU, EPHE-PSL, UA, 57 rue Cuvier, CP50, 75005 Paris, Francesylvain.gerber@mnhn.fr

Synopsis
The biological no�on of morphospace is examined from its conceptual and analy�caldimensions. We review the diverse morphospace geometries encountered in the literatureand their implica�ons for the interpreta�ons of morphological paterns. We also show how
considera�ons of organismal development suggest novel mathema�cal structures to endow
the set of morphological variants with evolu�onarily meaningful no�ons of accessibility.

Main text
The no�on of morphospace is both of conceptual and empirical importance in biology andpaleobiology. Conceptually, it has entailed cri�cal discussions about the rela�ve prevalence ofselec�ve forces, varia�onal constraints, and historical con�ngencies in shaping paterns ofmorphological evolu�on. Empirically, morphospaces have proven powerful quan�ta�ve tools
to document and analyze morphological paterns in various research areas, from compara�veanatomy and systema�cs, to func�onal morphology and large-scale studies of clade dynamics.
A morphospace is generally understood as the depic�on of morphological variants as points
in an abstract space in such a way that the rela�ve proximity of points expresses themorphological similarity of variants. Here, we discuss whether this way of conceiving
morphospace is always warranted in empirical studies or even adequate for all researchques�ons. Two main aspects pertaining to morphospace geometry are considered: (i) thepoten�al misinterpreta�on of the geometry induced by some morphometric descriptors and(ii) a no�on of evolu�onary accessibility among variants derived from the developmental
representa�on of morphological traits.
Morphospace narra�ves o�en include statements about distance (between morphologicalvariants) and direc�on (of morphological change) indica�ng that an inner-product geometry(generally the dot product of Euclidean geometry) is assumed for the morphospace. However,
not all morphospaces are equipped with the metric proper�es that one tends to intui�vely
atach to the no�on of ‘space’ [1,2]. So-called ‘theore�cal morphospaces’ are par�cularlyprone to such non-metric geometries [2]. Raup’s iconic shell coiling morphospace is taken as
an example to illustrate this phenomenon and discuss its implica�ons for biological inferences.
In paleobiology, the use of discrete character data does lead to metric morphospaces(assuming no missing data), but their Hamming-like geometry is some�mes overlooked [3]. In
par�cular, the morphospace and its mul�variate ordina�on are o�en confused for one another,invi�ng the use of inappropriate methodologies for their analyses (Fig. 1A).

Figure 1. (A) Morphospace representa�on from discrete character data; (B) Accessibility structure
mapped onto a morphospace.

Historically, methodological approaches to morphospace construc�on have typically aimed for
metric topologies deﬁned at the morphological level, organizing variants according to theirmorphological similarity. This choice may be subop�mal for addressing some importantevolu�onary ques�ons however, since morphological distance among variants can be a poor
predictor of their evolu�onary accessibility (Fig. 1B). We show how a gene�c or developmental
representa�on of morphological characters allows the deﬁni�on of accessibility among
variants and enriches the explanatory power of morphospace with regards to the role ofconstraints and selec�on in morphological evolu�on [4].
References[1] Huttegger, S. M., & Mitteroecker, P. (2011). Invariance and meaningfulness in phenotype
spaces. Evolutionary Biology, 38, 335-351.
[2] Gerber, S. (2017). The geometry of morphospaces: lessons from the classic Raup shellcoiling model. Biological Reviews, 92(2), 1142-1155.
[3] Gerber, S. (2019). Use and misuse of discrete character data for morphospace and disparity
analyses. Palaeontology, 62(2), 305-319.
[4] Gerber, S. (2014). Not all roads can be taken: development induces anisotropic accessibility
in morphospace. Evolution & Development, 16(6), 373-381.